On variant reflected backward SDEs, with applications.
Onsager-Machlup functionals for solutions of stochastic boundary-value problems
Optimal contracts in continuous-time models.
Optimal position targeting with stochastic linear-quadratic costs
We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate...
Optimal state estimation of a Markov process from point process observations
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimization of consumption with partial observation-Jensen inequality method
A solution to a model of optimal consumption with partial observation considered in [LOS] is presented. The approach is based on the Jensen inequality and does not require application of the filtering equation.
Option pricing in a CEV model with liquidity costs
The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar...
Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations.