Related papers: Optimal Multiple Stopping with Negative Discount R…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
In this note, merging ideas from Loeffen (2009) and Renaud (2019), we prove that an (a,b)-strategy maximizes dividend payments subject to fixed transaction costs in a spectrally negative L\'evy model with Parisian ruin, as long as the tail…
We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to…
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally…
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
We consider de Finetti's stochastic control problem for a spectrally negative L\'evy process in an Omega model. In such a model, the (controlled) process is allowed to spend time under the critical level but is then subject to a…
Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, $\textit{periodic}$ dividend strategies were recently introduced (Albrecher, Gerber…
In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric L\'evy process. We consider four contracts, three of which were…
We consider the general class of spectrally positive L\'evy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot…
We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders…
In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance…
We consider the non-linear optimal multiple stopping problem under general conditions on the non-linear evaluation operators, which might depend on two time indices: the time of evaluation/assessment and the horizon (when the reward or loss…
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…
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…
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…
Lewis and Mordecki have computed the Wiener-Hopf factorization of a L\'evy process whose restriction on $]0,+\infty[$ of their L\'evy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq…
In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller…
We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…
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…