Related papers: Contraction options and optimal multiple-stopping …
We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…
We consider a version of the stochastic inventory control problem for a spectrally positive L\'evy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are…
Motivated by recent developments in risk management based on the U.S. bankruptcy code, we revisit the De Finetti's optimal dividend problem by incorporating the reorganization process and regulator's intervention documented in Chapter 11…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…
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…
Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities,…
Sequential Bayesian experimental design typically assumes that the number of experiments is fixed before data collection begins. In practical campaigns, however, experimentation may need to terminate early because additional measurements…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
Using a new approach, for spectrally negative L\'evy processes we find joint Laplace transforms involving the last exit time (from a semi-infinite interval), the value of the process at the last exit time and the associated occupation time,…
In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when…
We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity averse decision maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or…
Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…