Related papers: Selling a stock at the ultimate maximum
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…
In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show…
In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned…
Given a stable L\'{e}vy process $X=(X_t)_{0\le t\le T}$ of index $\alpha\in(1,2)$ with no negative jumps, and letting $S_t=\sup_{0\le s\le t}X_s$ denote its running supremum for $t\in [0,T]$, we consider the optimal prediction problem…
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at…
In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…
Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At…
We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
The purpose of this paper is to showcase trading strategies that give solutions to three difficult and intriguing problems in business finance, economics and statistics. The paper discusses trading strategies for both commodities and stocks…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, by using a limit order or a market order. For a diffusive market, we characterize the optimal limit order…
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…
We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk…
We consider the problem of optimal inside portfolio $\pi(t)$ in a financial market with a corresponding wealth process $X(t)=X^{\pi}(t)$ modelled by \begin{align}\label{eq0.1} \begin{cases} dX(t)&=\pi(t)X(t)[\alpha(t)dt+\beta(t)dB(t)];…
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of…
In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at the origin, dividends give rise…
We consider an insurance company modelling its surplus process by a Brownian motion with drift. Our target is to maximise the expected exponential utility of discounted dividend payments, given that the dividend rates are bounded by some…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
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…