Related papers: Some results on optimal stopping problems for one-…
In N.V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
In this paper we introduce a numerical method for optimal stopping in the framework of one dimensional diffusion. We use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients.…
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…
In this paper, we investigate the boundedness of the imaginary powers of four generalized diffusion operators. This key property, which implies the maximal regularity property, allows us to solve both the linear and semilinear Cauchy…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…
In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to…
This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is…
In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, we solve the associated nonlinear eigenvalue problem for weakly coupled systems and…
In this paper we study pricing of American put options on the Black and Scholes market with a stochastic interest rate and finite-time maturity. We prove that the option value is a $C^1$ function of the initial time, interest rate and stock…
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…
This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion…
We consider an optimal stopping problem with n correlated offers where the goal is to design a (randomized) stopping strategy that maximizes the expected value of the offer in the sequence at which we stop. Instead of assuming to know the…
Score-based generative models (SGMs) have revolutionized the field of generative modeling, achieving unprecedented success in generating realistic and diverse content. Despite empirical advances, the theoretical basis for why optimizing the…
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal…
We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
A necessary and sufficient condition is obtained for the existence of strong stationary times for ergodic one-dimensional diffusions, whatever the initial distribution. The strong stationary times are constructed through intertwinings with…