Related papers: Some results on optimal stopping problems for one-…
Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
In Bai and Paulsen (SIAM J. Control optim. 48, 2010) the optimal dividend problem under transaction costs was analyzed for a rather general class of diffusion processes. It was divided into several subclasses, and for the majority of…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled 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…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
In this paper, we study the consumption-chemotaxis-Stokes model with porous medium slow diffusion in a three dimensional bounded domain with zero-flux boundary conditions and no-slip boundary condition. In recent ten years, many efforts…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game…
We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this…