Related papers: Selling a stock at the ultimate maximum
Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the…
We propose a recursive algorithm for the numerical computation of the optimal value function $\inf_{t\le\tau\le T} E \Big[\sup_{0\le s\le T } Y_s / Y_{\tau} \big| {\cal F}_t\Big]$ over the stopping times $\tau$ with respect to the…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric…
We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
This paper is concerned with an optimal strategy for simultaneously trading a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by the…
This paper studies the risk-adjusted optimal timing to liquidate an option at the prevailing market price. In addition to maximizing the expected discounted return from option sale, we incorporate a path-dependent risk penalty based on…
Given two probability measures $\mu, \nu$ on $\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\tau$ that maximize/minimize the cost functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$, where $(B_t)_t$ is…
Given the marginal distribution information of the underlying asset price at two future times $T_1$ and $T_2$, we consider the problem of determining a model-free upper bound on the price of a class of American options that must be…
In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…
We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional…
We analyze an irreversible investment decision for a project which yields a flow of future operating profits given by a geometric Brownian motion with unknown drift. In contrast to similar optimal stopping problems with incomplete…
A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques \`{a} la…
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…
We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this…
We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…