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Books > Science & Mathematics > Mathematics > Optimization
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Performance Bounds and Suboptimal Policies for Multi-Period Investment (Paperback)
Loot Price: R1,588
Discovery Miles 15 880
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Performance Bounds and Suboptimal Policies for Multi-Period Investment (Paperback)
Series: Foundations and Trends (R) in Optimization
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Examines dynamic trading of a portfolio of assets in discrete
periods over a finite time horizon, with arbitrary time-varying
distribution of asset returns. The goal is to maximize the total
expected revenue from the portfolio, while respecting constraints
on the portfolio like a required terminal portfolio and leverage
and risk limits. The revenue takes into account the gross cash
generated in trades, transaction costs, and costs associated with
the positions, such as fees for holding short positions. The model
that is presented takes the form of a stochastic control problem
with linear dynamics and convex cost function and constraints.
While this problem can be tractably solved in several special cases
- for example, when all costs are convex quadratic, or when there
are no transaction costs - the focus is on the more general case,
with nonquadratic cost terms and transaction costs. Performance
Bounds and Suboptimal Policies for Multi-Period Investment shows
how to use linear matrix inequality techniques and semidefinite
programming to produce a quadratic bound on the value function,
which in turn gives a bound on the optimal performance. This
performance bound can be used to judge the performance obtained by
any suboptimal policy. As a by-product of the performance bound
computation, an approximate dynamic programming policy is obtained
that requires the solution of a convex optimization problem, often
a quadratic program, to determine the trades to carry out in each
step.
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