January 2024
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8 Reads
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2 Citations
SSRN Electronic Journal
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Publications (60)
January 2024
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13 Reads
SSRN Electronic Journal
August 2023
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34 Reads
We propose the first discrete-time infinite-horizon dynamic formulation of the financial index tracking problem under both return-based tracking error and value-based tracking error. The formulation overcomes the limitations of existing models by incorporating the intertemporal dynamics of market information variables not limited to prices, allowing exact calculation of transaction costs, accounting for the tradeoff between overall tracking error and transaction costs, allowing effective use of data in a long time period, etc. The formulation also allows novel decision variables of cash injection or withdraw. We propose to solve the portfolio rebalancing equation using a Banach fixed point iteration, which allows to accurately calculate the transaction costs specified as nonlinear functions of trading volumes in practice. We propose an extension of deep reinforcement learning (RL) method to solve the dynamic formulation. Our RL method resolves the issue of data limitation resulting from the availability of a single sample path of financial data by a novel training scheme. A comprehensive empirical study based on a 17-year-long testing set demonstrates that the proposed method outperforms a benchmark method in terms of tracking accuracy and has the potential for earning extra profit through cash withdraw strategy.
January 2023
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5 Reads
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1 Citation
SSRN Electronic Journal
January 2023
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20 Reads
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1 Citation
SSRN Electronic Journal
January 2023
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14 Reads
SSRN Electronic Journal
September 2022
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42 Reads
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11 Citations
Operations Research
Endogenization of the Reference Point Reduces Loss Aversion A central idea in behavioral economics is that agents derive utility from gain and losses relative to a certain reference point and that losses loom larger than gains. In “How Endogenization of the Reference Point Affects Loss Aversion: A Study of Portfolio Selection,” He and Strub study the implications of various models of partially endogenous reference points on portfolio selection. In these models, an agent faces a salient exogenous reference point that influences the formation of endogenously determined expectations about the future, through rational expectations, optimal expectations, or mental updating of the reference point. A key finding is that the predictions of these models are identical to a model with an exogenous reference point but a lower degree of loss aversion. This suggests that it is difficult to separately identify an agent’s degree of loss aversion and his or her reference point and may help to explain why experienced and sophisticated agents appear to be less loss averse than expected in some field settings.
April 2022
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3 Reads
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12 Citations
Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intra-personal conflict but unable to commit herself in the future to following the optimal plan today, the rational strategy for her today is to reconcile with her future selves, namely to correctly anticipate her actions in the future and then act today accordingly. Such a strategy is named intra-personal equilibrium and has been studied since as early as in the 1950s. A rigorous treatment in continuous-time settings, however, had not been available until a decade ago. Since then, the study on intra-personal equilibrium for time-inconsistent problems in continuous time has grown rapidly. In this chapter, we review the classical results and some recent development in this literature.
March 2022
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112 Reads
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28 Citations
Annual Review of Statistics and Its Application
Risk measures are used not only for financial institutions’ internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk measure is a controversial issue. We review the literature on risk measures, particularly on issues such as subadditivity, robustness, elicitability, and backtesting. We also aim to clarify some misconceptions and confusions in the literature. In particular, we argue that, despite lacking some mathematical convenience, the median shortfall—that is, the median of the tail loss distribution—is a better option than the expected shortfall for setting the Basel Accords capital requirements due to statistical and economic considerations such as capturing tail risk, robustness, elicitability, backtesting, and surplus invariance. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
January 2022
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8 Reads
SSRN Electronic Journal
Citations (36)
... Prior literature has studied incentives in AMMs, but no prior work has simultaneously modeled and analyzed the following three properties of CLMMs: (1) LPs can only invest up to a fixed budget, (2) LPs in CLMMs can invest different amounts in different price ranges, and (3) LPs compete against each other for fees, and thus must take into account other LPs' strategies and their budgets [26]. Most existing works focus on the study of a single LP's strategy [23] or on the case where LPs are identical [10,23,24,29,30,35], and in both cases the budget is assumed to be unlimited [35]. For legacy AMMs, [35] proposes a framework using symmetric games to show the uniqueness of the symmetric Nash equilibrium. ...
- Citing Article
January 2024
SSRN Electronic Journal
... For example, Baron et al. (2015) study a newsvendor problem in which consumers are loss-averse with stochastic reference points that represent their beliefs about possible price and product availability. He and Strub (2022) study how the endogenization of stochastic reference points affects the portfolio optimization under loss aversion. Zhang and Li (2021) investigate the implications of loss aversion on firm profit, consumer surplus, and social welfare when firms endogenously make quality disclosure decisions. ...
- Citing Article
September 2022
Operations Research
... For the aspect of solving the respective DM problems, [9] appeared to be one of the first few works that establish a mathematical framework of subgame perfect equilibrium (SPE) on top of the ideas of [31,29,27]. The framework was then popularized since the seminal work of [2] on its application to MV portfolio selection, while [5,4,15,16,37,36,22] subsequently developed the analogous dynamic programming and maximum principle frameworks for characterizing the SPE; see also the review of [14]. Motivated by the significance of model uncertainty, a developing literature introduces the robust SPE that accounts for ambiguity and time inconsistency simultaneously; see [30,21,12,13]. ...
- Citing Chapter
April 2022
... In this situation, the corresponding Nash equilibrium control is not considered as a strong equilibrium strategy. (He & Jiang, 2021) investigate whether some classical time-consistent control problems have strong equilibrium strategies in the closed-loop Nash equilibrium, and find that the answer relies on the range of spike deviations. For the conventional MV portfolio problem, the time-consistent strategy is not a strong equilibrium strategy, if the spike deviation is allowed to be a general feedback function. ...
- Citing Article
October 2021
SIAM Journal on Control and Optimization
... Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtesting predictions, see e.g., Gneiting (2011) and . The literature on elicitability in risk management is extensive, with many authors arguing for its importance (Ziegel 2016, He et al. 2022. The characterisation of elicitable convex and coherent risk measures for example has been studied in Bellini and Bignozzi (2015), while showed that Expected Shortfall (ES) is jointly elicitable with VaR. ...
Reference:
Robust Elicitable Functionals
- Citing Article
March 2022
Annual Review of Statistics and Its Application
... There also have numerous extensions of the mean-risk portfolio optimization from the single-period setting to the dynamic, continuous-time one (e.g. Zhou and Li, 2000;Bielecki et al., 2005;Jin et al., 2005;Basak and Chabakauri, 2010;He et al., 2015;Zhou et al., 2017;Gao et al., 2017;Dai et al., 2021;He and Jiang, 2021). In particular, He et al. (2015) study a continuous-time mean-risk portfolio choice when risk is measured by the weighted Valueat-Risk (WVaR) but their results are rather pessimistic. ...
- Citing Article
July 2021
Mathematics of Operations Research
... By similar arguments in [5], it is easy to establish the verification theorem (Sufficiency) for the Markovian setting while the non-Markovian setting was attempted in [17]. The Necessity issue is difficult and we refer the readers to its latest progress, such as [33,17,15,11] and a comprehensive literature review of the field in [16]. ...
- Citing Article
January 2021
SSRN Electronic Journal
... 2 Other research that has addressed optimal payoff choices under symmetric distance constraints include works by Bernard et al. (2015b), Rüschendorf and Vanduffel (2020), and He and Jiang (2021). ...
- Citing Article
March 2021
Operations Research Letters
... Various applications of forward preferences have been explored, including equilibrium models [26], relative preferences [6,64], and insurance applications [18,52]. Further investigations include risk measures [20,65], indifference pricing [5,59], optimal liquidation strategies [60], long-term yield curve dynamics [23], behavioral finance [30], and pension policy [33]. ...
- Citing Article
January 2021
Mathematical Finance
... A follow-up study expands this model by introducing probability weighting and a convex-concave value function, providing further insights into the stock market non-participation and equity premium puzzles through the lens of narrow framing and cumulative prospect theory [10]. Another study further refined the model by assuming proportional effects of gains and losses on an agent's total utility [11]. ...
- Citing Article
January 2021
Journal of Mathematical Economics