On almost sure convergence of modified Euler-Peano approximation of solution to an S.D.E. driven by a semimartingale
On approximate large deviations for 1D diffusion.
On approximation of solutions to a class of stochastic equations.
On Backward Stochastic Differential Equations Approach to Valuation of American Options
We consider the problem of valuation of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. We show that the value function has two different but related representations: by means of a solution of some nonlinear backward stochastic differential equation, and by a weak solution to some semilinear partial differential equation.
On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes
The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô integrable stochastic processes in terms of their primitive processes.
On changes of measure in stochastic volatility models.
On compact Ito's formulas for martingales of mc4.
We prove that the class mc4 of continuous martingales with parameter set [0,1]2, bounded in L4, is included in the class of semi-martingales Sc∞(L0(P)) defined by Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this result with the compact Itô formula obtained by Sanz in [S] for martingales of mc4.
On convergence of population processes in random environments to the stochastic heat equation with colored noise.
On convergence of semimartingales
On convex stochastic processes.
On differential equations and inclusions with mean derivatives on a compact manifold
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
On equivalence of a class of random processes in Hilbert space and a Wiener process.
On equivalence of a process of diffusion type in Hilbert space and a Wiener process.
On equivalent martingale measures with bounded densities
On European option pricing under partial information
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...
On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
On Existence of Local Martingale Measures for Insiders who Can Stop at Honest Times
We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time Λ. We show, using the multiplicative decomposition of the Azéma supermartingale, that if the martingale part of the price process has the predictable representation property and Λ satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider. This...
On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
On extrapolation blowups in the scale.
On extremal solutions of martingale problems