相关论文: Optimal Multiple Stopping Problems under g-expecta…

The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…

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…

This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…

The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great…

We study the optimal stopping problem for a monotonous dynamic risk measure induced by a BSDE with jumps in the Markovian case. We show that the value function is a viscosity solution of an obstacle problem for a partial…

In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in…

We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…

Considering that the decision-making environment faced by reinforcement learning (RL) agents is full of Knightian uncertainty, this paper describes the exploratory state dynamics equation in Knightian uncertainty to study the…

In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous…

We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing…

We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an…

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…

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…

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…

This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…

In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We…