Chance-constrained portfolio selection is an approach to portfolio selection under

Loss aversion Loss aversion is the tendency to prefer avoiding losses to acquiring equivalent gains. The principle is prominent in the domain of economics. What distinguishes loss aversion from risk aversion is that the utility of a monetary payoff depends o ...

. The formulation assumes that investor’s preferences are representable by the

expected utility The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...

of final wealth, and that they require to be acceptably low, the probability of their final wealth falling below a survival or safety level. The chance-constrained portfolio problem is then to find: :Max

\sum_

w_jE(X_j), subject to Pr(

\sum_

w_jX_j < s) ≤ ,

\sum_

w_j = 1, w_j ≥ 0 for all j, ::where s is the survival level and is the admissible probability of ruin; w is the weight and x is the value of the ''jth'' asset to be included in the portfolio. The original implementation is based on the seminal work of

Abraham Charnes Abraham Charnes (September 4, 1917 – December 19, 1992) was an American mathematician who worked in the area of operations research. Charnes published more than 200 research articles and seven books, including ''An Introduction to Linear Progra ...

and

William W. Cooper William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr. Linear Programming".. He was the founding president of The Institute of Management Sciences, founding ...

on stochastic programming in 1959, and was first applied to finance by Bertil Naslund and Andrew B. Whinston in 1962 and in 1969 by N. H. Agnew, et al. For fixed the chance-constrained portfolio problem represents

Lexicographic preferences In economics, lexicographic preferences or lexicographic orderings describe comparative preferences where an agent prefers any amount of one good (X) to any amount of another (Y). Specifically, if offered several bundles of goods, the agent will ch ...

and is an implementation of capital asset pricing under loss aversion. In general though, it is observed that no

utility function As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...

can represent the preference ordering of chance-constrained programming because a fixed does not admit compensation for a small increase in {{math, ''α'' by any increase in expected wealth. For a comparison to mean-variance and safety-first portfolio problems, see; for a survey of solution methods here, see; for a discussion of the

risk aversion In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more c ...

properties of chance-constrained portfolio selection, see Pyle, D. H. and Stephen J. Turnovsky (1971), “Risk Aversion in Chance Constrained Portfolio Selection, Management Science,18, No. 3, 218-22

Retrieved September 24, 2020.

References

Portfolio theories Stochastic optimization Financial economics Actuarial science

See also

References