Optimal Portfolio Under State-Dependent Expected Utility

2018 ◽  
Author(s):  
Carole Bernard ◽  
Steven Vanduffel ◽  
Jiang Ye
Keyword(s):  
Expected Utility ◽  
Optimal Portfolio ◽  
State Dependent

OPTIMAL PORTFOLIO UNDER STATE-DEPENDENT EXPECTED UTILITY

2018 ◽  
Vol 21 (03) ◽  
pp. 1850013 ◽  
Author(s):  
CAROLE BERNARD ◽  
STEVEN VANDUFFEL ◽  
JIANG YE
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Loss Aversion ◽  
Reference Point ◽  
Joint Distribution ◽  
Optimal Portfolio ◽  
Characterization Result ◽  
Terminal Wealth ◽  
Utility Maximizer ◽  
State Dependent

We derive the optimal portfolio for an expected utility maximizer whose utility does not only depend on terminal wealth but also on some random benchmark (state-dependent utility). We then apply this result to obtain the optimal portfolio of a loss-averse investor with a random reference point (extending a result of Berkelaar et al. (2004) Optimal portfolio choice under loss aversion, The Review of Economics and Statistics 86 (4), 973–987). Clearly, the optimal portfolio has some joint distribution with the benchmark and we show that it is the cheapest possible in having this distribution. This characterization result allows us to infer the state-dependent utility function that explains the demand for a given (joint) distribution.

A Non‐Bayesian Theory of State‐Dependent Utility

Econometrica ◽  
2019 ◽  
Vol 87 (4) ◽  
pp. 1341-1366 ◽  
Author(s):  
Brian Hill
Keyword(s):  
Expected Utility ◽  
State Dependence ◽  
Comparative Statics ◽  
Bayesian Theory ◽  
Subjective Expected Utility ◽  
State Dependent ◽  
Special Cases

Many decision situations involve two or more of the following divergences from subjective expected utility: imprecision of beliefs (or ambiguity), imprecision of tastes (or multi‐utility), and state dependence of utility. This paper proposes and characterizes a model of uncertainty averse preferences that can simultaneously incorporate all three phenomena. The representation supports a principled separation of (imprecise) beliefs and (potentially state‐dependent, imprecise) tastes. Moreover, the representation permits comparative statics separating the roles of beliefs and tastes, and is modular: it easily delivers special cases involving various combinations of the phenomena, as well as state‐dependent multi‐utility generalizations covering popular ambiguity models.

scholarly journals ON THE OPTIMAL COMBINATION OF ANNUITIES AND TONTINES

2020 ◽  
Vol 50 (1) ◽  
pp. 95-129 ◽  
Author(s):  
An Chen ◽  
Manuel Rach ◽  
Thorsten Sehner
Keyword(s):  
Expected Utility ◽  
Optimal Combination ◽  
Optimal Portfolio ◽  
Longevity Risk ◽  
Retirement Income ◽  
The Novel ◽  
Retirement Plan

AbstractTontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity, but provides a less volatile retirement income than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: the previously introduced “tonuity”, a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity and an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine. Further, we derive conditions on the premium loadings of annuities and tontines indicating when the optimal portfolio is investing a positive amount in both annuity and tontine, and when the optimal portfolio turns out to be a pure annuity or a pure tontine.

scholarly journals Extended choice functionals - a cardinal framework for the analysis of choice under risk

2020 ◽  
Vol 15 ◽  
pp. 66-78
Author(s):  
Somdeb Lahiri ◽  
Keyword(s):  
Decision Making ◽  
Expected Utility ◽  
Choice Theory ◽  
Decision Aids ◽  
Social Choice Theory ◽  
Axiomatic Characterization ◽  
Managerial Decision ◽  
Evaluation Functions ◽  
State Dependent

We propose a framework that extends the one developed by Professor Amartya Sen (with Arrowian roots), for the analysis of choice under risk by an individual, hereafter referred to as a decision maker. The framework is based on the decision maker’s state dependent numerical evaluations − referred to as utility, worth, or pay-off − of the alternatives. We provide several examples to illustrate meaningful possibilities in the model proposed here. The expected utility choice functional assigns to each given state- -dependent data profile (i.e., a pair consisting of a profile of state-dependent evaluation functions and a probability distribution over states of nature) the non-empty set of alternatives obtained by maximizing expected utility. A significant result in this paper, which illustrates the workability of our frameworks of analysis, is an axiomatic characterization of the expected utility choice functional using purely combinatorial techniques. Aim/Purpose: To use a minor extension of the Arrow-Sen model of social choice theory to study individual decision making/aiding under risk and with state dependent evaluation functions. Methodology: Combinatorics (theory of finite sets). Findings: Plausible decision-aids for decision making under uncertainty with state dependent evaluation functions. Research Implications: Exactly same model and results apply for the study of “weighted” multi-criteria decision making/aiding with state dependent evaluation functions. Contribution: Apart from useful decision-aids for managerial decision making under risk and operations research, we provide an axiomatic characterization of the expected utility choice functional. Keywords: risk, state-dependent evaluation, extended choice functionals.

scholarly journals Ordering of Optimal Portfolio Allocations in a Model with a Mixture of Fundamental Risks

2008 ◽  
Vol 45 (01) ◽  
pp. 55-66 ◽  
Author(s):  
Ka Chun Cheung ◽  
Hailiang Yang
Keyword(s):  
Expected Utility ◽  
Optimal Portfolio ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
Likelihood Ratio Order ◽  
Portfolio Problem ◽  
Proposed Model ◽  
Special Cases ◽  
Optimal Allocations

In this paper we study a single-period optimal portfolio problem in which the aim of the investor is to maximize the expected utility. We assume that the return of every security in the market is a mixture of some common underlying source of risks. A sufficient condition to order the optimal allocations is obtained, and it is shown that several models studied in the literature before are special cases of the proposed model. In the course of the analysis concepts in stochastic orders are employed, and a new characterization of the likelihood ratio order is obtained.

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