Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach

Jin, Xing; Luo, Dan; Zeng, Xudong

doi:10.1287/moor.2017.0854

Cited by 13 publications

(6 citation statements)

References 36 publications

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“…with respect to P, where the process Λ ϕ (t) is modelled by the stochastic differential equation (see Jin et al [38]) 4 Mathematical Problems in Engineering…”

Section: E Wealth Processmentioning

confidence: 99%

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Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Deng

et al. 2020

Mathematical Problems in Engineering

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In this paper, we consider a robust optimal investment-reinsurance problem with a default risk. The ambiguity-averse insurer (AAI) may carry out transactions on a risk-free asset, a stock, and a defaultable corporate bond. The stock’s price is described by a jump-diffusion process, and both the jump intensity and the distribution of jump amplitude are uncertain, i.e., the jump is ambiguous. The AAI’s surplus process is assumed to follow an approximate diffusion process. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle, and the reinsurance type has to follow a self-reinsurance function. In performing dynamic programming, both the predefault case and the postdefault case are analyzed, and the optimal strategies and the corresponding value functions are derived under the worst-case scenario. Moreover, we give a detailed proof of the verification theorem and give some special cases and numerical examples to illustrate our theoretical results.

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“…with respect to P, where the process Λ ϕ (t) is modelled by the stochastic differential equation (see Jin et al [38]) 4 Mathematical Problems in Engineering…”

Section: E Wealth Processmentioning

confidence: 99%

“…But in most instances, the distribution of jump amplitude is unknown. Jin et al [38] considered the dynamic portfolio choice problem with ambiguous jump risks in a multidimensional jump-diffusion framework. In their results, both the jump amplitude distribution and the jump intensity were assumed to be uncertain.…”

Section: Introductionmentioning

confidence: 99%

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Deng

et al. 2020

Mathematical Problems in Engineering

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“…The agent is only concerned about misspecification of the jump process, a logical choice that we follow, since the probability distribution of rare events is by their very nature much harder to estimate compared to the diffusion component. Other papers on partial equilibrium portfolio choice models with ambiguity aversion and jump-diffusion processes are Jin, Luo, and Zeng (2017) and Branger and Larsen (2013). The first paper uses a nonparametric approach to model ambiguity aversion in the jump component, the second paper focuses on utility losses if ambiguity is ignored.…”

Section: Related Literaturementioning

confidence: 99%

Discounting the Future: on Climate Change, Ambiguity Aversion and Epstein-Zin Preferences

Olijslagers

Wijnbergen

2019

SSRN Journal

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We focus on the effect of preference specifications on the current day valuation of future outcomes. Specifically, we analyze the effect of risk aversion, ambiguity aversion and the elasticity of intertemporal substitution on the willingness to pay to avoid climate change risk. The first part of the paper analyzes a general disaster (jump) risk model with a constant arrival rate of disasters. This provides useful intuition in how preferences influence valuation of long-term risk. The second part of the paper extends this model with a climate model and a temperature dependent arrival rate. Since the model yields closed form solutions up to solving an integral, our model does not suffer from the curse of dimensionality of numerical IAMs with several state variables. Introducing Epstein-Zin preferences with an elasticity of substitution higher than one and ambiguity aversion leads to much larger estimates of the social cost of carbon than obtained under power utility. The dominant parameters are the risk aversion coefficient and the elasticity of intertemporal substitution. Ambiguity aversion is of second order importance. JEL codes: Q51, Q54, G12, G13 1 For a very different (and strongly worded) view focusing on the social welfare aspects of the rate of time preference rather than on individual preferences, see Chichilnisky, Hammond, and Stern (2018);Stern (2015) who look at a positive rate of time preference as discrimination between generations that happen to have been born at different moments in time.2 This list is not exhaustive, but is used to give an idea of the nature of an IAM. 3 The references do not contain the most recent versions of the IAMs.1. Power utility, no ambiguity aversion r 1 = r P ow − γλm − λ(e −γ(µ J − 1 2 γσ 2 J ) − 1) 2. SDU utility, no ambiguity aversion3. Power utility, ambiguity aversion r 3 = r SDU − γλ * m * − λ * (e −γ(µ J +b * σ 2 J − 1 2 γσ 2 J ) − 1) 4. SDU utility, ambiguity aversion r 4 = r

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“…The second strand discusses only jump ambiguity and is represented in studies by Jin et al. ( 2018 ), Aït-Sahalia and Matthys ( 2019 ), and Jin et al. ( 2021 ).…”

Section: Introductionmentioning

confidence: 99%

Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets

Pang

Xia

et al. 2023

Financ Innov

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In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the cryptocurrency market into a single framework. We reach the following conclusions in both markets: first, price diffusion and jump ambiguity mainly determine detection-error probability; second, optimal choice is more significantly affected by price diffusion ambiguity than by jump ambiguity, and trivially affected by volatility diffusion ambiguity. In addition, investors tend to be more aggressive in a stable market than in a volatile one. Next, given a larger volatility jump size, investors tend to increase their portfolio during downward price jumps and decrease it during upward price jumps. Finally, the welfare loss caused by price diffusion ambiguity is more pronounced than that caused by jump ambiguity in an incomplete market. These findings enrich the extant literature on effects of ambiguity on the traditional stock market and the evolving cryptocurrency market. The results have implications for both investors and regulators.

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Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach

Cited by 13 publications

References 36 publications

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Discounting the Future: on Climate Change, Ambiguity Aversion and Epstein-Zin Preferences

Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets

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