A technique for qualitatively synthesizing the structure of risk management vehicles

Abstract

In design, inferring structure from function is a generate-and-test problem that is subject to combinatorial explosion. For certain types of economic and physical systems, it is fruitful to specify function in terms of desired behavior, and to identify sets of structurally connected components whose combined behavior under specific operating conditions matches the desired behavior. Specifically, in the financial risk management domain, behaviors of the components (stocks, bonds, options, etc.) are specified by two-dimensional piecewise linear functions called “payoff profiles,” and the goal is to identify linear combinations of these functions that produce a constrained behavior in response to uncontrollable economic events (e.g., interest rate fluctuations). Each identified combination corresponds to a configuration of investment vehicles which provide that constrained behavior. This paper presents a qualitative synthesis technique which uses this concept to construct all configurations of investment vehicles with a given desired behavior. Because the space of linear combinations of two-dimensional piecewise linear functions is subject to combinatorial explosion, the technique constrains the generation of combinations using two means. One is a goal-directed search process that relies on knowledge pertaining to the additivity of piecewise linear functions. Another is a qualitative abstraction over all piecewise linear functions with a similar shape, combined with the use of heuristic synthesis operators that rediscover information lost due to the abstraction. The technique is currently applied in a prototype expert system that supports the entire design process of risk management vehicles. The paper also discusses the possibility of using the technique in physical domains, through the configuration of analog computers.