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The purpose of this paper is to argue that Bernoulli's “utility function solution to the St Petersburg paradox” was wrong and to find a new method to solve the paradox.

This goal is attained through two ways: using Bernoulli's and Kramer's utility function to construct new paradoxes; and designing and implementing a new St Petersburg game which does not carry the effect of diminishing marginal utility.

In this paper, the author finds that Bernoulli's “utility function solution to the St Petersburg paradox” was wrong, and also finds a new model to solve the paradox, which is also a brand‐new model of estimates under uncertainty.

Bernoulli put forward the diminishing marginal utility of currency and thus accordingly provided the utility function solution to solve the paradox. This paper indicates that the Bernoulli's utility function solution does not work. Thus, further research needs to be taken in several aspects: is the diminishing marginal utility of currency tenable? Does the marginal utility of currency decrease monotonically? Are concave utility functions represented by negative index functions which are widely used in theoretical study reasonable?

The paper proposes a brand‐new possible research idea and direction for economic theoretical researches based on uncertainty.

This paper proved the untenability of the utility function solution to solve the St Petersburg paradox for the first time and proposed the pioneering “risk adjustment model” of estimates under uncertainty.

Much of the literature on theories of decision making under risk has emphasized differences between theories. One enduring theme has been the attempt to develop a distinction between “normative” and “descriptive” theories of choice. Bernoulli (1738) introduced log utility because expected value theory was alleged to have descriptively incorrect predictions for behavior in St. Petersburg games. Much later, Kahneman and Tversky (1979) introduced prospect theory because of the alleged descriptive failure of expected utility (EU) theory (von Neumann & Morgenstern, 1947).

Events surrounding September 11, 2001, have motivated increasing interest in identifying, assessing, and managing the risk of “extreme events.” This article introduces a new mathematical framework for the risk management of extreme event risk. In the article, the author proposes criteria based on “higher” (the third and fourth) moments that dominate variance (the second moment) in explaining the economics of insurance and reinsurance. Economic and financial implications are then applied to the underwriting and investment activities of insurers and reinsurers.

The purpose of this paper is to benchmark alternatives of decision problems that include risk and uncertainty considering different risk attitudes via a new data envelopment analysis (DEA) decision model.

A new utility function of strict bounds is applied in a data envelopment model to evaluate all possible stochastic alternatives (i.e. gambles). The amount of risk in the alternatives is measured by a newly introduced risk ratio (RR). Each alternative is considered as a decision making unit (DMU). The alternatives efficiency frontier is found via linear optimization of the DEA model.

In contrast to literature studies of binary decision alternatives, here, benchmarking is conducted to evaluate multiple decision alternatives with unbounded utility of the payoffs along with a new DEA decision model. Different surveys and studies have been used to validate the model. DEA could demonstrate the ability to uncover relationships that remain hidden for other methodologies. The resulting rankings remarkably conform to those elicited by subjects.

Individuals of different wealth backgrounds evaluate risky decision problems differently.

The paper contributes to the existing research by benchmarking multiple alternatives as compared to the literature research which usually assesses binary problems. Instead of using explicit utilities, the model implements the efficiencies along with a new utility function and a new RR. The introduction of DEA to such a decision field is found to be successful in benchmarking numerous alternatives under different risk attitudes.

The dominant theory of individual decision making under uncertainty is the von Neumann and Morgenstern's expected utility model (EUM). Although, this model has gained its popularity from its ability to explain a wide range of attitudes toward risk, empirical evidence over the last three decades has documented paradoxical behavior that is inconsistent with the EUM model. The present study examines in an experimental setting individuals' inconsistent behavior in choosing between two pairs of lotteries known as the Allais paradox. This study extends previous literature on money gamble situations by conducting a series of experiments to test expected utility behavior on auditing student subjects in pure money and audit settings. Two variants of audit settings are examined: overall audit plan case and audit procedure evaluation of internal control case.

Menger disagreed with this view for various reasons. Also, the subjective expectation is infinite. There are many cases where man's behaviour fails to conform to mathematical expectations: games in which a player can win only one very large amount with a very small probability or games offering a single moderate amount with a very high probability. Furthermore, we can always find a sequence of payoffs x1, x2, x3,…, which yield infinite expected value, and then propose, say, that u(xn)=2ⁿ, so that expected utility is also infinite. Menger therefore proposed that utility must also be bounded above for paradoxes of this type to be resolved.

The market value of any property investment will tend to deteriorate over time when compared to similar modern properties if monies are not periodically expended to mitigate the effects of obsolescence. This paper examines the relationship between the initial yield of a property at purchase and the rate of future rental value growth necessary to achieve a criterion rate of return on the investment. Traditionally in calculations of the future rental growth rate required to justify an initial investment yield (when compared, say, to the rental shown by gilt‐edged stocks) the simplistic view is taken that following purchase no further expenditure is anticipated. However, if a property is to maintain its original market appeal (or adapt to evolving circumstances), capital must from time‐to‐time be injected for the purposes of refurbishment. Thus, any analytical model which ignores this inevitable expenditure, but nevertheless assumes a constant rate of long‐term future rental growth, is quite unrealistic. A Refurbishment‐Rental Growth Model is derived which allows the introduction of regular future capital expenditure both in terms of magnitude and frequency. Various examples are illustrated of the effect which such expenditure may have in necessarily increasing the required future rental growth for a property investment in order to achieve an anticipated level of return.

§ 1. My presentation to the Circle. When I presented my theory to the Circle, I found a mixed reception. Schlick, however, slightly shook his head, the mock-smile appeared on his face, and he tried to exchange glances. Only Waismann responded. Kaufmann was too loyal a friend to openly go against me even though he strongly felt that I was wrong. And Carnap was in deep thought.

A weighting or a rank‐dependent weighting function was used by revamped models of risky choice to explain that Allais Paradox arises because people behave so as to maximize overall value rather than EU. The risky choice behavior was, however, simply seen by the equate‐to‐differentiate model as a choice between the best possible outcomes or a choice between the worst possible outcomes. A “judging” task was designed to examine whether the knowledge of paired outcomes will permit prediction of preference. It was shown that the observed choices could be better accounted for by the equate‐to‐differentiate approach revealed by the judging data.

The prospect theory is potentially an essential ingredient in modeling the disposition effect. However, many scholars have tried to explain the disposition effect with the help of prospect theory and they came to opposite conclusions. The purpose of this paper is to examine the impact of value function of the prospect theory on predicting the disposition effect.

Lagrange multiplier optimization and dynamic programming method are used to solve the representative investor’s optimal portfolio choice problem. Furthermore, numerical simulation is used to compare the prediction ability of different types of value function.

The authors support that the value function has a crucial role in predicting the disposition effect with prospect theory, i.e. the curvature and boundedness of the value function may influence the performance of applying the prospect theory in the disposition effect. They conclude that a piecewise negative exponential value function can predict the disposition effect, while others like the piecewise power value function may not.

Extant literature about modeling the disposition effect with the prospect theory mostly focus on the time when gain-loss utility occurs or the selection of reference point. This paper based on the value function properties provides a new perspective in analyzing the crucial role that value function has in predicting financial market anomalies.