Related papers: Optimal liquidation trajectories for the Almgren-C…
In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the…
We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred…
A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many…
This paper studies the problem of optimally extracting nonrenewable natural resources. Taking into account the fact that the market values of the main natural resources i.e. oil, natural gas, copper,..., etc, fluctuate randomly following…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
We consider a class of infinite-time horizon optimal stopping problems for spectrally negative Levy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale…
We study a single risky financial asset model subject to price impact and transaction cost over an infinite horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in fixed…
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
We extend the Lindquist-Rachev (LR) option-pricing framework--which values derivatives in markets lacking a traded risk-free bond--by introducing common Levy jump dynamics across two risky assets. The resulting endogenous "shadow" short…
This paper investigates a dividend optimization problem with a positive creeping-associated terminal value at ruin for spectrally negative Levy processes. We consider an insurance company whose surplus process evolves according to a…
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…
The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected…
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…
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a…
This paper is concerned with the problem of finding the optimal of extraction policies of an oil field in light of various financial and economical restrictions and constraints. Taking into account the fact that the oil price in worldwide…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
We consider the bail-out optimal dividend problem under fixed transaction costs for a L\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to…
We study the optimal liquidation of a large position on Uniswap v2 and Uniswap v3 in discrete time. The instantaneous price impact is derived from the AMM pricing rule. Transient impact is modeled to capture either exponential or…
We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…