Bin Li

Bin Li
University of Waterloo | UWaterloo · Department of Statistics and Actuarial Science

PhD

About

47
Publications
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559
Citations

Publications

Publications (47)
Article
We study the last exit time that a spectrally negative Lévy process is below zero until it reaches a positive level b , denoted by $g_{\tau_b^+}$ . We generalize the results of the infinite-horizon last exit time explored by Chiu and Yin (2005) by incorporating a random horizon $\tau_b^+$ , which represents the first passage time above b . We deriv...
Preprint
This paper introduces an economic framework to assess optimal longevity risk transfers between institutions, focusing on the interactions between a buyer exposed to long-term longevity risk and a seller offering longevity protection. While most longevity risk transfers have occurred in the reinsurance sector, where global reinsurers provide long-te...
Article
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This paper considers an optimal stopping problem with weighted discounting, and the state process is modelled by a general exponential Lévy process. Due to the time inconsistency, we provide a new martingale method based verification theorem for the equilibrium stopping strategies. As an application, we generalize an investment problem with non-exp...
Article
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Research in classical ruin theory has largely focused on the rst passage time analysis of a surplus process below level 0. Recently, inspired by numerous applications in nance, physics, and optimization, there has been an accrued interest in the analysis of the last passage time (below level 0). In this paper, we aim to bridge the rst and the last...
Article
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This paper studies an optimal investment and reinsurance problem under the smooth ambiguity model proposed by Klibanoff et al. (2005). We assume the mean-variance criterion for risk preferences and constant absolute ambiguity aversion for ambiguity preferences. In light of time inconsistency, closed-form equilibrium investment and reinsurance strat...
Article
This paper focuses on capturing the impacts of leptokurtic phenomenon and heterogeneous preferences in higher moments on asset allocation. To achieve this, we propose a utility maximization asset allocation framework under the multivariate affine generalized hyperbolic (MAGH) asset prices dynamics. With the investor’s preference given by the expone...
Article
p>In this paper, we study the magnitude and the duration of deep drawdowns for the Lévy insurance risk model through the characterization of the Laplace transform of a related stopping time. Relying on a temporal approximation approach (e.g., Li et al. (2018)), the proposed methodology allows for a unified treatment of processes with bounded and un...
Article
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This paper studies an optimal reinsurance problem under the α-maximin mean-variance criterion proposed in Li et al. [13]. We generalize [13] by considering a full range of ambiguity preferences and allowing for general form reinsurance contracts. For equilibrium reinsurance strategies, we find that the excess-of-loss form is unique for ambiguity-av...
Article
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Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure) and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with more general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative Lévy processes [9, 20...
Article
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This paper proposes a novel high-water mark fee structure and investigates its impact on the marketability of variable annuities. To evaluate the welfare effects of holding a variable annuity, we set up a mean-variance preference model. By also examining the welfare effects of holding two alternative investments, a risk-free bond and a pure fund, w...
Article
In this paper, we study the magnitude and the duration of deep drawdowns for the Lévy insurance risk model through the characterization of the Laplace transform of a related stopping time. Relying on a temporal approximation approach (e.g., Li et al. (2018)), the proposed methodology allows for a unified treatment of processes with bounded and unbo...
Article
Full-text available
In this paper, we consider a dynamic Pareto optimal risk‐sharing problem under the time‐consistent mean‐variance criterion. A group of n insurers is assumed to share an exogenous risk whose dynamics is modeled by a Lévy process. By solving the extended Hamilton–Jacobi–Bellman equation using the Lagrange multiplier method, an explicit form of the ti...
Article
Insurance contracts pricing, that is determining the risk loading added to the expected loss, plays a fundamental role in insurance business. It covers the loss from adverse claim experience and generates a profit. As market competition is a key component in the pricing exercise, this paper proposes a novel dynamic pricing game model with multiple...
Article
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We study the optimal reinsurance-investment problem for the compound dynamic contagion process introduced by Dassios and Zhao (2011). This model allows for self-exciting and externally-exciting clustering effect for the claim arrivals, and includes the well-known Cox process with shot noise intensity and the Hawkes process as special cases. For tra...
Article
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In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are know...
Article
The time to ruin has been the primary focus of many ruin-related analyses, mainly due to its significance in the assessment of an insurer’s solvency risk. The finite-time ruin probability and more recently, the t-year deferred ruin probability have drawn considerable attention over the years. Embedded into the expected discounted penalty function (...
Preprint
Full-text available
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally negative L\'{e}vy risk processes. This result improves the existing literature in which only the Laplace transform...
Preprint
In this paper, we complement the existing literature on the occupation time in the red (below level $0$) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative L\'evy process. For both classes of processes, we derive an explicit expression for the distribution of such occupation time up to an ind...
Article
Full-text available
In the existing literature of robust utility maximization with ambiguity, agents are generally assumed to be extremely ambiguous-averse as they tend to only consider expected payoffs in the worst-case scenario. However, experimental studies have shown that agents' attitude to ambiguity is not systematically negative, and can even be ambiguity-seeki...
Preprint
Full-text available
Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure) and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative L\'evy processes -- see Av...
Article
Full-text available
We study equilibrium feedback strategies for a dynamic mean-variance problem of investing in a risky financial market. We assume the time horizon is random, and we consider both discrete-time and continuous-time frameworks. The random time horizon is assumed to have a distribution that is independent of the underlying asset processes. By applying s...
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This paper studies the potential (or resolvent) measures of spectrally negative Lévy processes killed on exiting (bounded or unbounded) intervals, when the underlying process is observed at the arrival epochs of an independent Poisson process. Explicit representations of these so-called Poissonian potential measures are established in terms of newl...
Article
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In this paper, we model an entity's surplus process X using the drawdown-based regime-switching (DBRS) dynamics proposed in [9]. We introduce the state-dependent termination time to the model, and provide rationale for its introduction in insurance contexts. By examining some related potential measures, we first derive an explicit expression for th...
Article
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In this paper, we propose a new approach to study the Parisian ruin problem for spectrally negative Lévy processes. Since our approach is based on a hybrid observation scheme switching between discrete and continuous observations, we call it a temporal approach as opposed to the spatial approximation approach in the literature. Our approach leads t...
Article
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In this paper, we investigate the robust utility maximization problems under both preferences of extremely ambiguity loving and ambiguity aversion. By a fundamental martingale characterization technique on nonlinear expectations, optimal investment strategies are explicitly solved in a general non-Markovian framework via backward stochastic differe...
Article
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Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of the first passage time of the...
Preprint
Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of the first passage time of the...
Article
Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization prob...
Article
Full-text available
In this paper, we derive and study a pair of optimal reinsurance-investment strategies under the two-sided exit framework which aims to (1) maximize the probability that the surplus reaches the target before ruin occurs over the time horizon (where is an independent exponentially distributed random time); (2) minimize the probability that ruin occu...
Article
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Inspired by the alpha maxmin expected utility, we propose a new class of mean-variance criteria, called alpha maxmin mean-variance criteria, and apply it to the reinsurance-investment problem. Our model allows the insurer to have different levels of ambiguity aversion (rather than only consider the extremely ambiguity-averse attitude as in the lite...
Article
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In this paper, we study some drawdown-related quantities in the context of the renewal insurance risk process with general interarrival times and phase-type distributed jump sizes. We make use of some recent results on the two-sided exit problem for the spectrally negative Markov additive process and a fluid flow analogy between certain queues and...
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Drawdown measures the decline of portfolio value from its historic high-water mark. In this paper, we study a lifetime investment problem aiming at minimizing the risk of drawdown occurrences. Under the Black-Scholes framework, we examine two …nancial market models: a market with two risky assets, and a market with a risk-free asset and a risky ass...
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This paper considers magnitude, asymptotics and duration of drawdowns for some L\'evy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative L\'evy processes using an approximation approach. For any spectrally negative L\'evy process whose scale functions are well-behaved at $0+$, we then study the...
Article
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Drawdowns measuring the decline in value from the historical running maxima over a given period of time are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focused on the side of severity by studying the first drawdown over a certain prespecified size. In this paper we extend the discu...
Article
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In this paper, we propose a new drawdown-based regime-switching (DBRS) Lévy insurance model in which the underlying drawdown process is used to model the level of financial distress over time, and trigger regime-switching transitions. By some analytical arguments, we derive explicit formulas for a generalized two-sided exit problem. We specifically...
Article
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We aim at quantitatively measuring the liquidation risk of a firm subject to both Chapters 7 and 11 of the US bankruptcy code. The firm value is modeled by a general time-homogeneous diffusion process in which the drift and volatility are level dependent and can be easily adjusted to reflect the state changes of the firm. An explicit formula for th...
Data
In this paper we adopt the perturbation approach of Landriault, Renaud and Zhou (2011) to find expressions for the joint Laplace transforms of occupation times for time-homogeneous diffusion processes. The expressions are in terms of solutions to the associated differential equations. These Laplace transforms are applied to study ruin-related probl...
Article
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We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probabilit...
Article
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In this letter, we present a new hierarchical clustering approach based on the evolutionary process of Amari's dynamical neural field model. Dynamical neural field theory provides a theoretical framework macroscopically describing the activity of neuron ensemble. Based on it, our clustering approach is essentially close to the neurophysiological na...

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