scholarly journals Estimation of Approximate Values of the Optimum Points on Efficient Portfolios Curve

2007 ◽  
Vol 6 (1) ◽  
pp. 99-106
Author(s):  
Henryk Kowgier
Keyword(s):  
Utility Functions ◽  
Exponential Utility ◽  
Efficient Portfolios

Estimation of Approximate Values of the Optimum Points on Efficient Portfolios Curve In the paper a method is found for estimating approximate optimum points on efficient portfolios curve (risk-profit) that are connected with exponential utility functions being very frequently preferred in practice by investors.

scholarly journals Chains of Reinsurance Revisited

1986 ◽  
Vol 16 (2) ◽  
pp. 77-88 ◽  
Author(s):  
Jean Lemaire ◽  
Jean-Pierre Quairiere
Keyword(s):  
Utility Functions ◽  
Exponential Utility ◽  
Pareto Optimal ◽  
Optimal Reinsurance ◽  
Special Case

AbstractChains of reinsurance were first modelled by Gerber, in a special case. It is shown that more general results can be obtained by applying Borch's theorem. The Pareto-optimal reinsurance indemnities are uniquely determined using the only assumption that the participating companies use exponential utility functions. A simple comparison then shows that Gerber's indemnities are not Pareto-optimal. Even if no assumption at all is introduced, the indemnities are shown to be closely linked to the risk aversions of the participants.

THE MINIMAL κ-ENTROPY MARTINGALE MEASURE

2012 ◽  
Vol 15 (05) ◽  
pp. 1250038 ◽  
Author(s):  
BARBARA TRIVELLATO
Keyword(s):  
Exponential Function ◽  
Power Law ◽  
Utility Functions ◽  
Exponential Utility ◽  
Martingale Measure ◽  
Standard Entropy ◽  
Martingale Measures ◽  
Minimal Entropy Martingale Measure ◽  
New Class ◽  
Parameter Deformation

We introduce the notion of κ-entropy (κ ∈ ℝ, |κ| ≤ 1), starting from Kaniadakis' (2001, 2002, 2005) one-parameter deformation of the ordinary exponential function. The κ-entropy is in duality with a new class of utility functions which are close to the exponential utility functions, for small values of wealth, and to the power law utility functions, for large values of wealth. We give conditions on the existence and on the equivalence to the basic measure of the minimal κ-entropy martingale measure. Moreover, we provide characterizations of its density as a κ-exponential function. We show that the minimal κ-entropy martingale measure is closely related to both the standard entropy martingale measure and the well known q-optimal martingale measures. We finally establish the convergence of the minimal κ-entropy martingale measure to the minimal entropy martingale measure as κ tends to 0.

scholarly journals The General Economic Premium Principle

1984 ◽  
Vol 14 (1) ◽  
pp. 13-21 ◽  
Author(s):  
Hans Bühlmann
Keyword(s):  
Risk Aversion ◽  
Utility Functions ◽  
Exponential Utility ◽  
Risk Averse ◽  
Existence Of Equilibrium ◽  
Easy Proof ◽  
Quantitative Results

AbstractWe give an extension of the Economic Premium Principle treated in Astin Bulletin, Volume 11 where only exponential utility functions were admitted. The case of arbitrary risk averse utility functions leads to similar quantitative results. The role of risk aversion in the treatment is essential. It also permits an easy proof for the existence of equilibrium.

scholarly journals Pareto Optimality and Equilibrium in an Insurance Market

2008 ◽  
Vol 38 (2) ◽  
pp. 441-459 ◽  
Author(s):  
Alexey Y. Golubin
Keyword(s):  
Risk Aversion ◽  
Existence Theorem ◽  
Pareto Optimality ◽  
Market Risk ◽  
Utility Functions ◽  
Economic Equilibrium ◽  
Exponential Utility ◽  
Insurance Market ◽  
Reinsurance Market

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch’s model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.

scholarly journals Pareto Optimality and Equilibrium in an Insurance Market

2008 ◽  
Vol 38 (02) ◽  
pp. 441-459 ◽  
Author(s):  
Alexey Y. Golubin
Keyword(s):  
Risk Aversion ◽  
Existence Theorem ◽  
Pareto Optimality ◽  
Market Risk ◽  
Utility Functions ◽  
Economic Equilibrium ◽  
Exponential Utility ◽  
Insurance Market ◽  
Reinsurance Market

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch’s model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.

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