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Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion

Borkowski D., Jańczak-Borkowska K.

Opuscula Mathematica

2018

Vol. 38, no. 3

307--326

We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.

On Backward Stochastic Differential Equations Approach to Valuation of American Options

Klimsiak T., Rozkosz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 3

275--288

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.

Infinite horizon reflected backward stochastic differential equations and applications in mixed control and game problems

Hamadène S., Lepeltier J.-P., Wu Z.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

211--234

We prove existence and uniqueness results of the solution for infinite horizon reflected backward stochastic differential equations with one or two barriers. We also apply these results to get the existence of optimal control strategy for the mixed control problem and a saddle-point strategy for the mixed game problem when, in both situations, the horizon is infinite.