Trading Regions Under Proportional Transaction Costs
نویسندگان
چکیده
In the Black-Scholes model optimal trading for maximizing expected power utility under proportional transaction costs can be described by three intervals B, NT , S: If the proportion of wealth invested in the stocks lies in B, NT , S, then buying, not trading and selling, respectively, are optimal. For a finite time horizon, the boundaries of these trading regions depend on time and on the terminal condition (liquidation or not). Following a stochastic control approach, one can derive parabolic variational inequalities whose solution is the value function of the problem. The boundaries of the active sets for the different inequalities then provide the boundaries of the trading regions. We use a duality based semi-smooth Newton method to derive an efficient algorithm to find the boundaries numerically.
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