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Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
In this paper, we investigate the robust optimal reinsurance,investment,and internal surplus distribution (i.e., consumption) problem for an insurer with Epstein-Zin recursive preferences in an incomplete market. It is assumed that the…
This paper presents an axiomatic approach to finite Markov decision processes where the discount rate is zero. One of the principal difficulties in the no discounting case is that, even if attention is restricted to stationary policies, a…
This paper deals with the general discounted impulse control problem of a piecewise deterministic Markov process. We investigate a new family of epsilon-optimal strategies. The construction of such strategies is explicit and only…
We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly…
Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a…
For continuing environments, reinforcement learning (RL) methods commonly maximize the discounted reward criterion with discount factor close to 1 in order to approximate the average reward (the gain). However, such a criterion only…
The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…
We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…
In this paper, we consider the Cox--Ingersoll--Ross (CIR) process in the regime where the process does not hit zero. We construct additive and multiplicative discrete approximation schemes for the price of asset that is modeled by the CIR…
The present paper addresses the issue of the stochastic control of the optimal dynamic reinsurance policy and dynamic dividend strategy, which are state-dependent, for an insurance company that operates under multiple insurance lines of…
We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish…
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\gamma$…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
We study a stochastic differential game in a ruin theoretic environment. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it,…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…