Related papers: An analytic recursive method for optimal multiple …
We consider de Finetti's problem for spectrally one-sided L\'evy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of…
In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…
In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by L\'{e}vy processes. The underlying numerical schemes are based on jump-adapted Euler schemes.…
This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
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 optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
This paper studies an optimal stopping problem for L\'evy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a…
We apply the Monte Carlo method to solving the Dirichlet problem of linear parabolic equations with fractional Laplacian. This method exploit- s the idea of weak approximation of related stochastic differential equations driven by the…
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…
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…
The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
For linear inverse problems $Y=\mathsf{A}\mu+\xi$, it is classical to recover the unknown signal $\mu$ by iterative regularisation methods $(\widehat \mu^{(m)}, m=0,1,\ldots)$ and halt at a data-dependent iteration $\tau$ using some…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation…
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently…