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In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products…
We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including…
Motivated by the asset-liability management of a nuclear power plant operator, we consider the problem of finding the least expensive portfolio, which outperforms a given set of stochastic benchmarks. For a specified loss function, the…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the…
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates…
In this work we study a finite horizon optimal liquidation problem with multiplicative price impact in algorithmic trading, using market orders. We analyze the case when an agent is trading on a market with two financial assets, whose…
In this work we address the problem of finding feasible policies for Constrained Markov Decision Processes under probability one constraints. We argue that stationary policies are not sufficient for solving this problem, and that a rich…
An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
A deep BSDE approach is presented for the pricing and delta-gamma hedging of high-dimensional Bermudan options, with applications in portfolio risk management. Large portfolios of a mixture of multi-asset European and Bermudan derivatives…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis…