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Absolutely continuous laws of Jump-Diffusions in finite and infinite dimensions with applications to mathematical Finance

Forster, Barbara; Luetkebohmert, Eva; Teichmann, Josef
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.69%
In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional It\^{o}-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently regular density. In this article we first prove results on absolute continuity for laws of projected jump-diffusion processes in finite and infinite dimensions, and a general result on the existence of Malliavin weights in finite dimension. In both cases we assume H\"ormander conditions and hypotheses on the invertibility of the so-called linkage operators. The purpose of this article is to show that for the construction of numerical procedures for the calculation of the Greeks in fairly general jump-diffusion cases one can proceed as in a pure diffusion case. We also show how the given results apply to infinite dimensional questions in mathematical Finance. There we start from the Vasi\v{c}ek model, and add -- by pertaining no arbitrage -- a jump diffusion component. We prove that we can obtain in this case an interest rate model, where the law of any projection is absolutely continuous with respect to Lebesgue measure on $\mathbb{R}^M $.; Comment: final version accepted for publication in SIAM Journal of Mathematical Analysis

Degenerate elliptic operators in mathematical finance and Holder continuity for solutions to variational equations and inequalities

Feehan, Paul M. N.; Pop, Camelia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.78%
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and H\"older continuity near the boundary for solutions to variational equations defined by the elliptic Heston operator, as well as H\"older continuity up to the boundary for solutions to variational inequalities defined by the elliptic Heston operator. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.; Comment: 68 pages, 3 figures

GPGPUs in computational finance: Massive parallel computing for American style options

Pagès, Gilles; Wilbertz, Benedikt
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/01/2011 Português
Relevância na Pesquisa
55.77%
The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming principle for such optimal stopping or stochastic control problems in a Markovian framework. Unfortunately, these Least-Square Monte Carlo approaches are rather slow and allow, due to the dependency structure in the Backward Dynamic Programming principle, no parallel implementation; whether on the Monte Carlo levelnor on the time layer level of this problem. We therefore present in this paper a quantization method for the computation of the conditional expectations, that allows a straightforward parallelization on the Monte Carlo level. Moreover, we are able to develop for AR(1)-processes a further parallelization in the time domain, which makes use of faster memory structures and therefore maximizes parallel execution. Finally, we present numerical results for a CUDA implementation of this methods. It will turn out that such an implementation leads to an impressive speed-up compared to a serial CPU implementation.

The financial framework of the sustainability of health universal coverage in Italy. A quantitative financial model for the assessment of the italian stability and reform program of public health financing

Olgiati, Stefano; Danovi, Alessandro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/07/2012 Português
Relevância na Pesquisa
55.72%
Italy and the Eurozone are heading in the year 2012 into a financial depression of unprecedented magnitude, with a forthcoming multitude of often contradictory public economic and financial stability emergency interventions whose ultimate endogenous and exogenous effects on public and private health spending and on the sustainability of universal coverage are difficult to predict ex ante. The research question is to assess whether it is possible to synthesise into a single and simple quantitative index such multitude of public economic and financial stability interventions and assess their magnitude and direction towards increasing or decreasing sustainability of publicly funded health care and universal coverage. We have analyzed the Italian Economic and Stability Reform Program 2011-2014 and we have proposed a quantitative synthetic sustainability index {\sigma} based on simple partial and absolute differential equations. The sustainability index {\sigma} highlights that in case the growth of the GDP in the period 2011-2014 be insufficient - as is already the case in the first semester of 2012 - all the assumptions on which the Italian Economic and Stability Reform Program 2011-2014 rests will fall, and Universal Coverage will become unsustainable. Health and Public Health professionals should intervene immediately with Italian and Eurozone national budgets planners and financial health regulators before unselective exogenously induced health financing and provision shortages produce irreparable epidemiological effects.; Comment: 28 pages

To the problem of turbulence in quantitative easing transmission channels and transactions network channels at quantitative easing policy implementation by central banks

Ledenyov, Dimitri O.; Ledenyov, Viktor O.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.74%
In agreement with the recent research findings in the econophysics, we propose that the nonlinear dynamic chaos can be generated by the turbulent capital flows in both the quantitative easing transmission channels and the transaction networks channels, when there are the laminar turbulent capital flows transitions in the financial system. We demonstrate that the capital flows in both the quantitative easing transmission channels and the transaction networks channels in the financial system can be accurately characterized by the Reynolds numbers. We explain that the transition to the nonlinear dynamic chaos regime can be realized through the cascade of the Landau, Hopf bifurcations in the turbulent capital flows in both the quantitative easing transmission channels and the transaction networks channels in the financial system. We completed the computer modeling, using both the Nonlinear Dynamic Stochastic General Equilibrium Theory (NDSGET) and the Hydrodynamics Theory (HT), to accurately characterize the US economy in the conditions of the QE policy implementation by the US Federal Reserve. We found that the ability of the US financial system to adjust to the different levels of liquidity depends on the nonlinearities appearance in the QE transmission channels...

Robust Quantitative Comparative Statics for a Multimarket Paradox

Harks, Tobias; von Falkenhausen, Philipp
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.69%
We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually reduce the monopolist's profit. We use our approach to quantify for the first time the worst case profit reduction for multimarket oligopolies exposed to arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies, we show that the relative profit loss of any firm is at most 25% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on social welfare. We find tight bounds also for these measures showing that total profit and social welfare decreases by at most 25% and 16.6%, respectively. Finally, we show that in our model, mixed, correlated and coarse correlated equilibria are essentially unique, thus, all our bounds apply to these game solutions as well.; Comment: 23 pages, 1 figure

A New Kind of Finance

Maymin, Philip Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/10/2012 Português
Relevância na Pesquisa
55.67%
Finance has benefited from the Wolfram's NKS approach but it can and will benefit even more in the future, and the gains from the influence may actually be concentrated among practitioners who unintentionally employ those principles as a group.; Comment: 13 pages; Forthcoming in "Irreducibility and Computational Equivalence: 10 Years After Wolfram's A New Kind of Science," Hector Zenil, ed., Springer Verlag, 2013

Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance

Kononovicius, Aleksejus; Gontis, Vygintas; Daniunas, Valentas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.67%
We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirman and Bass diffusion of new products are considered in this contribution as two basic ideas. Further we demonstrate that general herding behavior can be considered as a background of nonlinear stochastic model of financial fluctuations.; Comment: 20 pages, 8 figures

Pricing, liquidity and the control of dynamic systems in finance and economics

Willis, Geoff
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/05/2011 Português
Relevância na Pesquisa
55.67%
The paper discusses various practical consequences of treating economics and finance as an inherently dynamic and chaotic system. On the theoretical side this looks at the general applicability of the market-making pricing approach to economics in general. The paper also discuses the consequences of the endogenous creation of liquidity and the role of liquidity as a state variable. On the practical side, proposals are made for reducing chaotic behaviour in both housing markets and stock markets.

On three filtering problems arising in mathematical finance

Brigo, Damiano; Hanzon, Bernard
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/12/2008 Português
Relevância na Pesquisa
55.67%
Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral exchange rate news, by R. Mahieu, and P. Schotman; 2) A state space approach to estimate multi-factors CIR models of the term structure of interest rates, by A.L.J. Geyer, and S. Pichler; 3) Risk-minimizing hedging strategies under partial observation in pricing financial derivatives, by P. Fischer, E. Platen, and W. J. Runggaldier; In the first problem we propose to use a recent nonlinear filtering technique based on geometry to estimate the volatility time series from observed bilateral exchange rates. The model used here is the stochastic volatility model. The filters that we propose are known as projection filters, and a brief derivation of such filters is given. The second problem is introduced in detail, and a possible use of different filtering techniques is hinted at. In fact the filters used for this problem in 2) and part of the literature can be interpreted as projection filters and we will make some remarks on how more general and possibly more suitable projection filters can be constructed. The third problem is only presented shortly.; Comment: A short version appeared in "Insurance. Mathematics and Economics"...

Schr\"odinger group and quantum finance

Romero, Juan M.; Lavana, Ulises; Martínez, Elio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/04/2013 Português
Relevância na Pesquisa
55.67%
Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\"odinger algebra representation is constructed.; Comment: 10 page, non figures

Magic points in finance: Empirical integration for parametric option pricing

Gaß, Maximilian; Glau, Kathrin; Mair, Maximilian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.67%
We propose an interpolation method for parametric option pricing tailored to the persistently recurring task of pricing liquid financial instruments. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpolation method of Barrault et al. (2004) to parametric Fourier pricing. For a large class of combinations of option types, models and free parameters the approximation converges exponentially in the degrees of freedom and moreover has explicit error bounds. Numerical experiments confirm our theoretical findings and show a significant gain in efficiency, even for examples beyond the scope of the theoretical results. This is especially promising for further applications of the method.

L\'evy Processes For Finance: An Introduction In R

Manuge, D. J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/03/2015 Português
Relevância na Pesquisa
55.67%
This brief manuscript provides an introduction to L\'evy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular L\'evy processes are presented in R.; Comment: 18 pages, 9 figures

Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

Feehan, Paul M. N.; Pop, Camelia A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.78%
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given $C^\infty$-smooth data, we prove $C^\infty$-regularity of solutions up to the portion of the boundary where the operator is degenerate. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.; Comment: 55 pages, 1 figure. To appear in Advances in Differential Equations. Incorporates final galley proof corrections corresponding to published version

Quantitative easing is an incomplete strategy that must be accompanied by the nullification of debt

Svozil, Karl
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.69%
Compound interest as well as inflation grows exponentially with time, whereas other means to repay debt grow polynomially. For this and other, mostly political, reasons, debt without inflation is unsustainable. We suggest a discontinuous way to eliminate debt by nullifying it. This scenario is preferable to current central bank strategies of quantitative easing because it allows the disposal of debt without hyperinflation or bloated balance sheets.; Comment: 8 pages, some revisions

Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

Homescu, Cristian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/07/2011 Português
Relevância na Pesquisa
55.67%
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calculate these sensitivities. When compared to finite difference approximation, this approach can potentially reduce the computational cost by several orders of magnitude, with sensitivities accurate up to machine precision. Examples and a literature survey are also provided.; Comment: 23 pages

Multilevel Monte Carlo methods for applications in finance

Giles, Mike; Szpruch, Lukasz
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/12/2012 Português
Relevância na Pesquisa
55.67%
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and suggests directions for future research.; Comment: arXiv admin note: text overlap with arXiv:1202.6283; and with arXiv:1106.4730 by other authors

Quantitative relations between corruption and economic factors

Shao, Jia; Ivanov, Plamen Ch.; Podobnik, Boris; Stanley, H. Eugene
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/05/2007 Português
Relevância na Pesquisa
55.69%
We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investments per capita. These relations hold for diverse countries, and also remain stable over different time periods. We also observe a negative correlation between level of corruption and long-term economic growth. We find similar results for two independent indices of corruption, suggesting that the relation between corruption and wealth does not depend on the specific measure of corruption. The functional relations we report have implications when assessing the relative level of corruption for two countries with comparable wealth, and for quantifying the impact of corruption on economic growth and foreign investments.; Comment: 10 pages, 9 figures

Convex duality in stochastic programming and mathematical finance

Pennanen, Teemu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/06/2010 Português
Relevância na Pesquisa
55.69%
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.

Nonlinear PDEs risen when solving some optimization problems in finance, and their solutions

Itkin, Andrey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/10/2015 Português
Relevância na Pesquisa
55.84%
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the properties of these PDEs. We also demonstrate how to solve them numerically in a general case, and analytically in some particular case.; Comment: 20 pages, 3 figs