Singular recursive utility

We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular recursive utility. We derive sufficient and necessary maximum principles for this problem, and connect it to the Skorohod reflection problem. Finally, we apply our results to a specific cash flow. In this case, we find that the optimal consumption rate is given by the solution to the corresponding Skorohod reflection problem

Managing uncertainty:financial, actuarial and statistical modelling.

present value; Value; Actuarial;

Stochastic Volterra equations with time-changed L\'evy noise and maximum principles

We study an optimal control problem for Volterra type dynamics driven by time-changed L\'evy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative as introduced in [7]. We prove both a stochastic sufficient and necessary maximum principle and we complete the work providing applications to optimal portfolio problems

Mean-Field Optimal Control of Di¤usion with Regime Switching

The objective of this thesis is to study a problem of optimal control with regime switching jump-di¤usion model of mean-…eld type. In the …rst part we recall a result in the stochastic maximum principle whose horizon is …nite. In the second part, we devote ourselves to presenting the two main results of this thesis, in the …rst result we give the necessary and su¢ cient conditions of optimality whose control system is governed by a stochastic di¤erential equation with regime switching of in…nite horizon and by way of illustration, we have given two examples where in both cases the equation of state is linear and the objective function is of utility form. The second contribution on the maximum principle for a control problem of conditional mean …eld type of …nite horizon, we illustrate our result by a model which gives an explicit solutio

Stochastics of Environmental and Financial Economics

Systems Theory, Contro