Related papers: A primer of optimal ergodic average control for an…
In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend…
We prove a ratio ergodic theorem for amenable equivalence relations satisfying a strong form of the Besicovich covering property. We then use this result to study general non-singular actions of non-abelian free groups and establish a ratio…
Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk…
We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between "put" and "call" in the portfolio such that the average gain is almost always positive for a generic…
This paper proposes a supervised training algorithm for learning stochastic resource allocation policies with generative diffusion models (GDMs). We formulate the allocation problem as the maximization of an ergodic utility function subject…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
Risk-sensitive control balances performance with resilience to unlikely events in uncertain systems. This paper introduces ergodic-risk criteria, which capture long-term cumulative risks through probabilistic limit theorems. By ensuring the…
We study the optimal scheduling problem for a Markovian multiclass queueing network with abandonment in the Halfin--Whitt regime, under the long run average (ergodic) risk sensitive cost criterion. The objective is to prove asymptotic…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
In the classical static optimal reinsurance problem, the cost of capital for the insurer's risk exposure determined by a monetary risk measure is minimized over the class of reinsurance treaties represented by increasing Lipschitz retained…
In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is…
This paper presents a whole-body robot control method for exploring and probing a given region of interest. The ergodic control formalism behind such an exploration behavior consists of matching the time-averaged statistics of a robot…
A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its…
A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for…
This paper examines optimal risk sharing for empirically realistic risk attitudes, providing results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Contrary to common…
To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that…
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed…
Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with…