Related papers: On a Monotone Dynamic Approach to Optimal Stopping…

In this paper we provide a theoretical analysis of Variable Annuities with a focus on the holder's right to an early termination of the contract. We obtain a rigorous pricing formula and the optimal exercise boundary for the surrender…

A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…

In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…

This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov…

Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we…

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…

This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

This paper presents a simple algorithm to check whether reachability probabilities in parametric Markov chains are monotonic in (some of) the parameters. The idea is to construct - only using the graph structure of the Markov chain and…

We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…

In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…

In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…

We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…

For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…

We consider the optimal stopping problem consisting in, given a strong Markov process, a reward function and a discount rate, finding the stopping time such that the expected reward at the stopping time is maximum. The approach we follow,…

This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…

Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the…

We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game…

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…