18,080 research outputs found
Recommended from our members
Developments in linear and integer programming
In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies
Recommended from our members
Migration, credit markets, moral hazard, interlinkage.
A fast numerical algorithm is developed to price European options with
proportional transaction costs using the utility maximization framework
of Davis (1997). This approach allows option prices to be computed by
solving the investor's basic portfolio selection problem, without the inser-
tion of the option payo into the terminal value function. The properties
of the value function can then be used to drastically reduce the number of
operations needed to locate the boundaries of the no transaction region,
which leads to very e cient option valuation. The optimization problem
is solved numerically for the case of exponential utility, and comparisons
with approximately replicating strategies reveal tight bounds for option
prices even as transaction costs become large. The computational tech-
nique involves a discrete time Markov chain approximation to a continuous
time singular stochastic optimal control problem. A general de nition of
an option hedging strategy in this framework is developed. This involves
calculating the perturbation to the optimal portfolio strategy when an
option trade is execute
- …