SSRN Author: Xue Dong HeXue Dong He SSRN Content
https://privwww.ssrn.com/author=1346556
https://privwww.ssrn.com/rss/en-usWed, 20 Jan 2021 01:18:51 GMTeditor@ssrn.com (Editor)Wed, 20 Jan 2021 01:18:51 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: A New Preference Model That Allows for Narrow FramingNarrow framing is the idea that, when considering a monetary risk, the individual evaluates it to some extent in isolation and separately from her other risks. Originally documented in experimental settings, narrow framing has been widely applied to explain real-world investor behavior. We show that a prominent mathematical model of narrow framing presented in Barberis and Huang (2009, J. Econ. Dynam. Control, vol. 33, no. 8, pp. 1555--1576) has some drawbacks that limit its applicability. We then propose a new model of narrow framing that overcomes these limitations and show its tractability in applications to choice over monetary gambles.
https://privwww.ssrn.com/abstract=2903619
https://privwww.ssrn.com/1981894.htmlTue, 19 Jan 2021 09:06:47 GMTNew: Optimal Payoff under the Generalized Dual Theory of ChoiceWe consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The payoff of the optimal portfolio is a digital option: it yields an in-the-money payoff when the market is good and zero payoff otherwise. When the initial wealth increases, the set of good market scenarios remains unchanged while the payoff in these scenarios increases. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff and derive similar results.
https://privwww.ssrn.com/abstract=3722538
https://privwww.ssrn.com/1977297.htmlTue, 05 Jan 2021 17:31:11 GMTREVISION: Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability DistortionWe introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the ...
https://privwww.ssrn.com/abstract=3364750
https://privwww.ssrn.com/1976495.htmlSat, 02 Jan 2021 10:37:52 GMTREVISION: A New Preference Model That Allows for Narrow FramingNarrow framing is the idea that, when considering a monetary risk, the individual evaluates it to some extent in isolation and separately from her other risks. Originally documented in experimental settings, narrow framing has been widely applied to explain real-world investor behavior. We show that a prominent mathematical model of narrow framing presented in Barberis and Huang (2009, J. Econ. Dynam. Control, vol. 33, no. 8, pp. 1555--1576) has some drawbacks that limit its applicability. We then propose a new model of narrow framing that overcomes these limitations and show its tractability in applications to choice over monetary gambles.
https://privwww.ssrn.com/abstract=2903619
https://privwww.ssrn.com/1975029.htmlMon, 28 Dec 2020 10:34:56 GMTREVISION: Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal WealthIn a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of her terminal wealth must exceed a target and minimizes the variance of her terminal wealth. The agent can revise her expected terminal wealth target dynamically to adapt to the change of her current wealth, and we consider the following three targets: (i) the agent's current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent's current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent's current wealth and a pre-set aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of her wealth subject to a certain ...
https://privwww.ssrn.com/abstract=3084657
https://privwww.ssrn.com/1964584.htmlMon, 23 Nov 2020 11:10:02 GMTREVISION: On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous TimeIn a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature, referred to as weak equilibrium, is not fully aligned with the standard definition of equilibrium in the game theory in that the agent may be willing to deviate from a given weak equilibrium strategy. To address this issue, Huang and Zhou (2019, forthcoming in Mathematics of Operations Research) propose the notion of strong equilibrium for an infinite-time stochastic control problem in which an agent can control the generator of a time-homogeneous, continuous-time, finite-state Markov chain at each time. We study weak and strong equilibrium in a general diffusion framework, provide necessary conditions for a strategy to be a strong equilibrium, and prove that strong equilibrium strategies do not exist for four investment and consumption problems. Finally, we propose a new notion of equilibrium strategies, referred to as regular equilibrium, show that it ...
https://privwww.ssrn.com/abstract=3308274
https://privwww.ssrn.com/1942520.htmlFri, 18 Sep 2020 08:21:33 GMTNew: Portfolio Selection under Median and Quantile MaximizationIn this paper, we study a portfolio selection problem in which an agent trades a risk-free asset and multiple risky assets with deterministic mean return rates and volatility and wants to maximize the alpha-quantile of her wealth at some terminal time. Because of the time inconsistency caused by quantiles, we consider intra-personal equilibrium strategies. We find that among the class of time-varying, affine portfolio strategies, the intra-personal equilibrium does not exist when alpha>1/2, leads to zero investment in the risky assets when alpha<1/2, and is a portfolio insurance strategy when alpha=1/2. We then compare the intra-personal equilibrium strategy in the case of alpha=1/2, namely under median maximization, to some other strategies and apply it to explain why more wealthy people invest more precentage of wealth in risky assets. Finally, we extend our model to account for multiple terminal time.
https://privwww.ssrn.com/abstract=3657661
https://privwww.ssrn.com/1933956.htmlThu, 20 Aug 2020 15:35:36 GMTNew: Dynamic Mean-Variance Efficient Fractional Kelly Portfolios in a Stochastic Volatility ModelFractional Kelly portfolios are popular investment strategies in the market. In this paper, we improve the mean-variance efficiency of a fractional Kelly portfolio by minimizing the variance of the return of a portfolio subject to the constraint that the expected return rate of the portfolio is as high as that of the fractional Kelly portfolio. We consider so-called equilibrium portfolio strategies due to time inconsistency caused by the mean-variance criterion. We drive an equilibrium strategy in closed form and show that it reduces the variance of portfolio return compared to the fractional Kelly portfolio, although the reduction is quantitatively small.
https://privwww.ssrn.com/abstract=3670621
https://privwww.ssrn.com/1933954.htmlThu, 20 Aug 2020 15:33:44 GMTREVISION: How Endogenization of the Reference Point Affects Loss Aversion: A Study of Portfolio SelectionWe study the implications of various models of reference point formation on optimal decision making in the context of portfolio optimization under loss aversion. If the reference point is exogenously given, then the predictions of any such model crucially depend on the choice of the reference point. On the other hand, if the reference point were fully endogenously determined, then loss aversion would not affect choice behavior, which is in violation of the empirical evidence. We thus consider the partially endogenous model of De Giorgi and Post [Management Science 57 (6):1094--1110, 2011], where the reference point is determined in equilibrium but contains an exogenous component. We find that optimal trading behavior is as if the reference point were completely exogenous and that allowing for a mental adjustment of the reference point solely manifests itself in a lower degree of loss aversion. We then propose two novel models of reference point formation: A model of a mentally ...
https://privwww.ssrn.com/abstract=3318295
https://privwww.ssrn.com/1906623.htmlTue, 09 Jun 2020 08:40:28 GMTREVISION: Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities IssuanceWe provide a characterization of comparative weak risk aversion and comparative RDEU risk aversion for RDEU preferences and, in particular, we correct a claim made by Quiggin (1993) regarding comparative RDEU risk aversion. We then apply the analysis of comparative risk aversion to a problem of optimal design of underwriting contracts in securities issuance. Specifically, in public offerings of equity, an investment banking rm (the underwriter) plays an insurance role: through the underwriting contract, the issuing rm transfers the issue risk to the underwriter, as would an insured to an insurer. We extend a classical model proposed by Mandelker and Raviv (1977) to situations where the issuing rm and the underwriter have RDEU preferences. Assuming that the issuing company's and the underwriter's utility functions are concave and linear, respectively, and that either the underwriter is risk neutral or both the issuing company and underwriter are strongly risk averse, we show that a ...
https://privwww.ssrn.com/abstract=3101176
https://privwww.ssrn.com/1906549.htmlTue, 09 Jun 2020 08:11:11 GMTREVISION: On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous TimeIn a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature, referred to as weak equilibrium, is not fully aligned with the standard definition of equilibrium in the game theory in that the agent may be willing to deviate from a given weak equilibrium strategy. To address this issue, Huang and Zhou (2019, forthcoming in Mathematics of Operations Research) propose the notion of strong equilibrium for an infinite-time stochastic control problem in which an agent can control the generator of a time-homogeneous, continuous-time, finite-state Markov chain at each time. We study weak and strong equilibrium in a general diffusion framework, provide necessary conditions for a strategy to be a strong equilibrium, and prove that strong equilibrium strategies do not exist for four investment and consumption problems. Finally, we propose a new notion of equilibrium strategies, referred to as regular equilibrium, show that it ...
https://privwww.ssrn.com/abstract=3308274
https://privwww.ssrn.com/1884855.htmlMon, 13 Apr 2020 08:40:02 GMTREVISION: Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability DistortionWe introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the ...
https://privwww.ssrn.com/abstract=3364750
https://privwww.ssrn.com/1875680.htmlSat, 14 Mar 2020 09:12:05 GMTREVISION: Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities IssuanceWe provide a characterization of comparative weak risk aversion and comparative RDEU risk aversion for RDEU preferences and, in particular, we correct a claim made by Quiggin (1993) regarding comparative RDEU risk aversion. We then apply the analysis of comparative risk aversion to a problem of optimal design of underwriting contracts in securities issuance. Specifically, in public offerings of equity, an investment banking firm (the underwriter) plays an insurance role: through the underwriting contract, the issuing firm transfers the issue risk to the underwriter, as would an insured to an insurer. We extend a classical model proposed by Mandelker and Raviv (1977) to situations where the issuing firm and the underwriter have RDEU preferences. Assuming that the issuing company's utility function is more concave than the underwriter's, we derive the optimal contract in closed form and show that a firm-commitment contract is optimal if and only if the issuing company's probability ...
https://privwww.ssrn.com/abstract=3101176
https://privwww.ssrn.com/1868806.htmlSat, 22 Feb 2020 09:45:20 GMT