Related papers: Optimal liquidation trajectories for the Almgren-C…
We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give…
In this paper we derive the optimal execution trajectory for a trader who wishes to buy or sell a large position of shares which evolve as a geometric Brownian process in contrast to the arithmetic model which prevails in the existing…
In this paper, we study de Finetti's optimal dividend problem with capital injection under the assumption that the dividend strategies are absolutely continuous. In many previous studies, the process before being controlled was assumed to…
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules…
We solve the superhedging problem for European options in an illiquid extension of the Black-Scholes model, in which transactions have transient price impact and the costs and the strategies for hedging are affected by physical or cash…
Suppose Xt is either a regular exponential type Levy process or a Levy process with a bounded variation jumps measure. The distribution of the extrema of Xt play a crucial role in many financial and actuarial problems. This article employs…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo…
In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as…
We study the problem of optimal portfolio selection in an illiquid market with discrete order flow. In this market, bids and offers are not available at any time but trading occurs more frequently near a terminal horizon. The investor can…
We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality…
In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that…
In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…
In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
We consider an optimal dividend problem with transaction costs where the surplus is modelled by a spectrally negative L\'evy process in an Omega model. n this model, the surplus is allowed to spend time below the critical ruin level, but is…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
In this paper we investigate an optimal dividend problem with transaction costs, where the surplus process is modelled by a refracted L\'evy process and the ruin time is considered with Parisian delay. Presence of the transaction costs…