``When in a difficult situation, it is sometimes better to give up and start all over again.'' While this empirical truth has been regularly observed wide range of circumstances, quantifying the effectiveness such heuristic strategy remains an open challenge. In paper, we combine notions optimal control stochastic resetting address problem. The emerging analytical framework allows one not only ...

Abstract. The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case that the value function is assumed to be continuous in time and once differentiable in the space variable (C) instead of once differentiable in time and twice in space (C), like in the classical resul...

This paper considers some measure-valued processes {Xt : t ∈ [0, T ]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Φ of the process are given that imply that the expectations E(Φ(XT )) are comparable to the constant branching case. Ap...

The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

This paper presents applications of stochastic control theory in determining an insurer's optimal reinsurance and rating policy. Optimality is defined by means of variances of such variables as underwriting result of the insurer, solvency margins of the insurer and reinsurer and the premiums paid by policyholders.

In this paper we develop a framework for optimal investment decisions for insurance companies under unhedgeable risk. The perspective that we choose is from an insurance company that tries to maximise the stream of dividends paid to its shareholders. The policy instruments that the company has are the dividend policy and the investment policy. The insurance company can continue to pay dividends...

This paper presents a computationally feasible procedure for the optimal control and stochastic simulation of large nonlinear models with rational expectations under the assumption of certainty equivalence.

Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in [17], whenever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic control problems. As an illustration, we show, within ...