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Levy and Levy (2002, 2004) extend the stochastic dominance (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S-shaped and reverse S-shaped (RS-shaped) utility functions, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests for risk seekers. In this paper, we extend their work by developing new statistics for both PSD and MSD of the first three orders. These statistics provide a tool to examine the preferences of investors with S-shaped utility functions proposed by Kahneman and Tversky (1979) in their prospect theory and investors with RS-shaped investors proposed by Markowitz (1952a). We also derive the limiting distributions of the test statistics to be stochastic processes. In addition, we propose a bootstrap method to decide the critical points of the tests and prove the consistency of the bootstrap tests. To illustrate the applicability of our proposed statistics, we apply them to study the preferences of investors with the corresponding S-shaped and RS-shaped utility functions vis-à-vis returns on iShares and vis-à-vis returns of traditional stocks and Internet stocks before and after the Internet bubble.

Levy and Wiener (J Risk Uncertain 16 (2), 147–163, 1998), Levy and Levy (Manage Sci 48 (10), 1334–1349, 2002; Rev Fin Stud 17 (4), 1015–1041, 2004) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be ‘the opposite of’ or ‘the same as’ their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.

We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.

As an important link of marine dumping management, reasonable selection of the location of temporary marine dumping areas is of great significance to the high-quality development of the marine economy. To solve the problem of multi-attribute decision-making (MADM) for the location selection of temporary marine dumping areas, firstly, a fuzzy ELECTRE II model based on S-shaped utility function and the combined weight of game theory was proposed, which fully considered the direct influence of human bounded rationality and combination weight on the decision-making results. In the next part, based on constructing the evaluation index system of the preselected location of the temporary marine dumping marines, the fuzzy ELECTRE II model is applied to the q-order orthopair fuzzy environment to rank the alternative locations of the temporary marine dumping areas. Finally, the effectiveness and advantages of the model are proved compared with other existing methods. This paper provides a new and effective framework for the location selection of temporary marine dumping areas and possesses reference significance for marine dumping management.

Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortions, a necessary condition for the optimality is derived. The results are applied to a few examples.

Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortions, a necessary condition for the optimality is derived. The results are applied to a few examples.

Based on measurements among 332 owner–managers, we investigate how the global shape of the utility function (i.e., S–shaped versus concave or convex over the total range of outcomes) relates to choice behavior. We find that the global shape of the utility function differs across decision makers (about one–third of the owner–managers exhibit an S–shaped utility function) and that the global shape is linked to organizational behavior (i.e., the production system employed), a result that does not change when using different methods to identify the decision maker's global shape of the utility function. The decision maker's risk attitude (risk averse or risk seeking) does not affect the choice of the production system. Whereas the degree of risk aversion, based on the local shape of the utility function, may be important in explaining owner–managers' trading behavior (Pennings and Smidts 2000), more structural organizational behavior appears to be linked to the global shape of the utility function.

Portfolio insurance strategies that ensure a certain minimum portfolio value or floor such as the Constant Proportion Portfolio Insurance (CPPI) and the Option-based Portfolio Insurance are economically important and widely spread among the banking and insurance industries. In distress and volatile market environments, investors such as pension funds have a need to insure their portfolios against downside risk in order to meet certain future payments or liabilities. Non-anticipated shocks or negative interest rates, jumps, crashes, or overnight trading restrictions in stock prices could drop pension fund portfolios below desired levels (present value of pension obligations) making them underfunded with pension assets to pension liabilities ratio below 100%. In particular, within the current low interest rate environment, a high number of pension funds happen to be underfunded which is a severe practical problem. Because of such scenarios, there is a need for an investment strategy which covers both the case of funded and underfunded portfolios. This article introduces a novel strategy which generalizes the CPPI approach. It has the overall target of guaranteeing the investment goal or floor while participating in the performance of the assets and limiting the downside risk of the portfolio at the same time. We show that the strategy accounts for behavioral aspects of the investor such as distorted probabilities, a risk-averse behavior for gains, and a risk-seeking behavior for losses. The proposed strategy turns out to be optimal within the Cumulative Prospect Theory framework by Tversky and Kahneman (J Risk Uncertain 5(4):297–323, 1992).

A risk-neutral producer faces liquidity constraint that forces him to liquidate real assets in imperfect markets if he cannot meet his cash obligation, entailing a fixed liquidation cost. Under this risk of liquidation, the risk-neutral producer is shown to refuse to undertake a risky project with positive expected excess return, exhibiting first-order risk aversion. The optimal output level of the producer is piecewise linear in wealth; it decreases or increases depending on whether the expected excess return is positive or negative. The producer's apparent utility function exhibits an S-shaped curve when the initial liquid assets are affected by a background risk that is normally distributed.

The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S -shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semimartingales, we derive sufficient and necessary conditions for the well-posedness of the optimisation problem in the case of piecewise-power probability distortion and utility functions. Finally, under straightforwardly verifiable conditions, we further demonstrate the existence of an optimal strategy.