501 research outputs found
When to Sell or Hold a Stock:Empirical Evidence from an Emerging Market
Data from an emerging market were used to determine when to sell or hold a stock for a single model of a stock whose price is assumed to be a geometric Brownian motion in which the jump Markov process changes back and forth between positive and negative values
Analysis of the optimal exercise boundary of American put option with delivery lags
We show that an American put option with delivery lags can be decomposed as a
European put option and another American-style derivative. The latter is an
option for which the investor receives the Greek Theta of the corresponding
European option as the running payoff, and decides an optimal stopping time to
terminate the contract. Based on the this decomposition, we further show that
the associated optimal exercise boundary exists, and is a strictly increasing
and smooth curve. We also analyze its asymptotic behavior for both large
maturity and small time lag using the free-boundary method.Comment: 28 pages, 5 figure
Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints
This paper considers utility indifference valuation of derivatives under
model uncertainty and trading constraints, where the utility is formulated as
an additive stochastic differential utility of both intertemporal consumption
and terminal wealth, and the uncertain prospects are ranked according to a
multiple-priors model of Chen and Epstein (2002). The price is determined by
two optimal stochastic control problems (mixed with optimal stopping time in
the case of American option) of forward-backward stochastic differential
equations. By means of backward stochastic differential equation and partial
differential equation methods, we show that both bid and ask prices are closely
related to the Black-Scholes risk-neutral price with modified dividend rates.
The two prices will actually coincide with each other if there is no trading
constraint or the model uncertainty disappears. Finally, two applications to
European option and American option are discussed.Comment: 28 pages in Science China Mathematics, 201
On the Application of Martingale theory to Investment Strategy
Most often than not, an investor holding stock
must decide whether to sell or keep holding the stock. This
investment strategy over the years appears to be an easy task
to take. In the investment parlance, it is called the Broker’s
Common Sense (BCS). We have shown in this paper that the
so-called BCS strategy is backed with advanced
mathematical (probabilistic) phenomenon; we used the
martingale theory to describe the strateg
Pairs Trading: An Optimal Selling Rule with Constraints
The focus of this paper is on identifying the most effective selling strategy
for pairs trading of stocks. In pairs trading, a long position is held in one
stock while a short position is held in another. The goal is to determine the
optimal time to sell the long position and repurchase the short position in
order to close the pairs position. The paper presents an optimal pairs-trading
selling rule with trading constraints. In particular, the underlying stock
prices evolve according to a two dimensional geometric Brownian motion and the
trading permission process is given in terms of a two-state {trading allowed,
trading not allowed} Markov chain. It is shown that the optimal policy can be
determined by a threshold curve which is obtained by solving the associated HJB
equations (quasi-variational inequalities). A closed form solution is obtained.
A verification theorem is provided. Numerical experiments are also reported to
demonstrate the optimal policies and value functions
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