Quadratic Convergence for Valuing American Options Using a Penalty Method
SIAM Journal on Scientific Computing
Stock Trading: An Optimal Selling Rule
SIAM Journal on Control and Optimization
Recursive Algorithms for Stock Liquidation: A Stochastic Optimization Approach
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
A Model for Reversible Investment Capacity Expansion
SIAM Journal on Control and Optimization
Trading a mean-reverting asset: Buy low and sell high
Automatica (Journal of IFAC)
Finite Horizon Optimal Investment and Consumption with Transaction Costs
SIAM Journal on Control and Optimization
Continuous-Time Markowitz's Model with Transaction Costs
SIAM Journal on Financial Mathematics
Two-Time-Scale Approximation for Wonham Filters
IEEE Transactions on Information Theory
Methods for Pricing American Options under Regime Switching
SIAM Journal on Scientific Computing
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This paper is concerned with the optimality of a trend following trading rule. The idea is to catch a bull market at its early stage, ride the trend, and liquidate the position at the first evidence of the subsequent bear market. We characterize the bull and bear phases of the markets mathematically using the conditional probabilities of the bull market given the up to date stock prices. The optimal buying and selling times are given in terms of a sequence of stopping times determined by two threshold curves. Numerical experiments are conducted to validate the theoretical results and demonstrate how they perform in a marketplace.