Helsinki University of TechnologySystems Analysis Laboratory

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Dynamic Portfolio Selection under Dynamic Portfolio Selection under

Uncertainty –Uncertainty –Theory and Its Applications to R&D valuationTheory and Its Applications to R&D valuation

Mean-Risk Utility TheoryMean-Risk Utility Theory

Janne Gustafsson

Systems Analysis Laboratory

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Helsinki University of TechnologySystems Analysis Laboratory

Status of Doctoral StudiesStatus of Doctoral Studies

1 article published in a conference proceedings– PRIME Decisions

2 articles in review– Contingent Portfolio Programming (CPP)– Mean-Risk Utility Theory

» closely related to CPP’s objective function

2 manuscripts under work– Case study on R&D project selection and real options valuation– Dynamic choice under risk

» further work on CPP’s objective function

Visit to London Business School in January-April 2003

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Helsinki University of TechnologySystems Analysis Laboratory

Mean-Risk Utility Theory – ProblemMean-Risk Utility Theory – Problem

Maurice Allais: DM should consider the entire probability distribution of (Jevonsian) utility

– Actual outcomes of lotteries are irrelevant, because they do not reflect desirability– Risk must be related to the dispersion of utility

Expected Utility Theory: DM considers expectation of utility only– Based on Independence Axiom– Why do we need this axiom?

» There are also other as appealing axioms as independence (e.g., betweenness)

Contradiction?– Concepts of utility different?– Does a von Neumann-Morgenstern utility function account for dispersion of

Jevonsian utilities?– Are there any more general implications?

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Helsinki University of TechnologySystems Analysis Laboratory

Earlier ApproahcesEarlier Approahces

Independence Axiom has been challenged– Allais (1953) first by critisizing the sole use of expectation– Empirical studies later showed several violations of EUT

Result: Several non-expected utility theories– Allais (1953): Positive Theory– Kahneman and Tversky (1979): Prospect Theory– MacCrimmon and Chew (1979): Weighted Utility Theory– Quiggin (1982): Rank-dependent Expected Utility Theory– Machina (1982): Generalized Expected Utility Analysis– Yaari (1987): Dual Theory– Chew, Epstein, and Segal (1991): Quadratic Utility Theory– Choquet expected utility models, and many more...

Yet, rarely used– most are mathematically challenging– a part of the axioms are typically unintuitive

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Helsinki University of TechnologySystems Analysis Laboratory

Aim and ResultsAim and Results

Aim: To show that risk attitude is related to dispersion of utilities Cannot by accomplished by using EUT => Need for new approach

– Use of several new techniques» e.g., preferences over consequences in the analysis of preferences over lotteries

– A set of 5 assumptions / axioms

Preference model: – CE is the DM’s certainty equivalent operator

» some real-valued functional that is consistent with stochastic dominance» e.g., CE[X] = E[X] – λ·LSAD[X]

– u is a measurable (Jevonsian) utility function» based on algebraic or positive difference structure

Under EUT:

( ) ( )V CE u CE u x y x y

vNMu h u 1( ) ( )uCE u h E h u x x

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Helsinki University of TechnologySystems Analysis Laboratory

Manuscript and PublicationManuscript and Publication

Manuscript was written alone, but there were helpful discussions with various persons at SAL

Quite long; some 64 pages– extensive comparison to various approaches to choice under risk– detailed motivation of the assumptions made

Manuscript submitted to an economic journal in August 2002– other authors had published many articles on the subject there– seemed to be the most appropriate publishing forum, should the theory

prove correct– no decision made to date