The problem of controlling a near-Hamiltonian noisy system so as to keep it within a domain of bounded oscillations is considered. An exponential risk-sensitive residence time criterion is introduced as a performance measure. An averaging procedure is developed to obtain the asymptotic solution of the optimal control problem. It is shown that the averaged HJB equation is reduced to a first orde...

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance like strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic vari...

Abstract Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely Hamilton–Jacobi–Bellman (HJB) equation. In general, this cannot be solved analytically, thus numerical algorithms are only tools provide accurate approximations. The aims paper is introduce novel fitted finite volume method solve high dimensional degenerated HJB from stochastic control...

The celebrated optimal portfolio theory of R. C. Merton was successfully extended by the author to assets that do not obey Log-Normal price dynamics in [S. Stojanovic, Computational Financial Mathematics using Mathematica® : optimal trading in stocks and options, Birkhäuser, Boston, 2003]. Namely, a general one-factor model was solved, and applied in the case of appreciation-rate reversing mark...

5 We present efficient partial differential equation (PDE) methods for continuous time mean6 variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. 7 The standard formulation of mean-variance optimal portfolio allocation problems, where the 8 total wealth is the underlying stochastic process, gives rise to a one-dimensional (1-D) non-linear 9 Hamilton-J...

We study several aspects of covariance control problems over martingale processes in Rd with constraints on the terminal distribution, arising from the theory of repeated games with incomplete information. We show that these control problems are the limits of discrete-time stochastic optimization problems called problems of maximal variation of martingales meaning that sequences of optimizers f...

Constitutive activation of the Janus kinase (JAK)/signal transducer and activator of transcription (STAT) pathway occurs frequently in cancer cells and contributes to oncogenesis. Among the members of STAT family, STAT3 plays a pivotal role in the development and progression of human tumors. The STAT3-mediated signaling pathway has been recognized as a promising anticancer target. Here, we show...

• An extension of the deep Galerkin method (DGM) to solve Fokker–Planck PDEs keeping probability density constraints automatically satisfied. A novel application policy iteration algorithm (PIA) together with DGM HJB equations. Additional applications system coupled equations (arising from stochastic games) and mean-field Game PDE (coupled Fokker Planck). Both extensions are applicable multidim...

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if the optimal control satisfies an exponential moment condition or if the value function is continuous on the closure of its domain. The key idea is to ...

1 Under the assumption that two asset prices follow an uncertain volatility model, the maximal and 2 minimal solution values of an option contract are given by a two dimensional Hamilton-Jacobi-Bellman 3 (HJB) PDE. A fully implicit, unconditionally monotone finite difference numerical scheme is developed 4 in this paper. Consequently, there are no time step restrictions due to stability conside...