Related papers: Optimal Annuitization with stochastic mortality: P…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function $f$ and our current net worth as $X(t)$ for any $t$, we invest an amount $f(X(t))$ in the market. We need a fortune of $M$…
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a…
We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
We revisit closed-loop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite time horizon which is generated by a Partially Observable Markov Decision Process (POMDP). The certainty equivalent…
This paper considers optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
The energy and material processing industries are traditionally characterized by very large-scale physical capital that is custom-built with long lead times and long lifetimes. However, recent technological advancement in low-cost…
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…
This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…
The state-of-the-art proposes Life Care Annuities, that have been recently designed as variable annuity contracts with Long-Term Care payouts and Guaranteed Lifelong Withdrawal Benefits. In this paper, we propose more general features for…
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{\'e}r-Lundberg…