Bin Li

Bio: Bin Li is an academic researcher from University of Waterloo. The author has contributed to research in topics: Drawdown (hydrology) & Drawdown (economics). The author has an hindex of 12, co-authored 38 publications receiving 396 citations. Previous affiliations of Bin Li include University of Iowa & University of Hong Kong.

On magnitude, asymptotics and duration of drawdowns for Lévy models

Abstract: June 30, 2015AbstractThis paper considers magnitude, asymptotics and duration of drawdowns for some L´evyprocesses. First, we revisit some existing results on the magnitude of drawdowns for spec-trally negative L´evy processes using an approximation approach. For any spectrally negativeL´evy process whose scale functions are well-behaved at 0+, we then study the asymptotics ofdrawdown quantities when the threshold of drawdown magnitude approaches zero. We alsoshow that such asymptotics is robust to perturbations of additional positive compound Poissonjumps. Finally, thanks to the asymptotic results and some recent works on the running max-imum of L´evy processes, we derive the law of duration of drawdowns for a large class of L´evyprocesses (with a general spectrally negative part plus a positive compound Poisson structure).The duration of drawdowns is also known as the “Time to Recover” (TTR) the historical max-imum, which is a widely used performance measure in the fund management industry. We findthat the law of duration of drawdowns qualitatively depends on the path type of the spectrallynegative component of the underlying L´evy process.Keywords: Asymptotics; Drawdown; Duration; L´evy process; Magnitude; Parisian stoppingtimeMSC(2000): Primary 60G40; Secondary 60G51

The joint Laplace transforms for diffusion occupation times

Abstract: 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 problems for several classes of diffusion risk processes.

On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models

Abstract: This paper considers magnitude, asymptotics and duration of drawdowns for some Levy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Levy processes using an approximation approach. For any spectrally negative Levy process whose scale functions are well-behaved at $0+$, we then study the asymptotics of drawdown quantities when the threshold of drawdown magnitude approaches zero. We also show that such asymptotics is robust to perturbations of additional positive compound Poisson jumps. Finally, thanks to the asymptotic results and some recent works on the running maximum of Levy processes, we derive the law of duration of drawdowns for a large class of Levy processes (with a general spectrally negative part plus a positive compound Poisson structure). The duration of drawdowns is also known as the "Time to Recover" (TTR) the historical maximum, which is a widely used performance measure in the fund management industry. We find that the law of duration of drawdowns qualitatively depends on the path type of the spectrally negative component of the underlying Levy process.

On minimizing drawdown risks of lifetime investments

Abstract: 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 financial market models: a market with two risky assets, and a market with a risk-free asset and a risky asset. Closed-form optimal trading strategies are derived under both models by utilizing a decomposition technique on the associated Hamilton–Jacobi–Bellman (HJB) equation. We show that it is optimal to minimize the portfolio variance when the fund value is at its historic high-water mark. Moreover, when the fund value drops, the proportion of wealth invested in the asset with a higher instantaneous rate of return should be increased. We find that the instantaneous return rate of the minimum lifetime drawdown probability (MLDP) portfolio is never less than the return rate of the minimum variance (MV) portfolio. This supports the practical use of drawdown-based performance measures in which the role of volatility is replaced by drawdown.

Equilibrium Strategies for the Mean-Variance Investment Problem over a Random Horizon

Abstract: 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 c...

Stochastic Differential Equations

Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Lévy processes and infinitely divisible distributions

Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

The Laplace Transform

Abstract: THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

High-Water Marks and Hedge Fund Management Contracts

Abstract: Incentive or performance fees for money managers are frequently accompanied by high-water mark provisions which condition the payment of the performance fee upon exceeding the maximum achieved share value. In this paper, we show that hedge fund performance fees are valuable to money managers, and conversely represent a claim on a significant proportion of investor wealth. The high-water mark provisions in these contracts limit the value of the performance fees. We provide a closed-form solution to the high-water mark

Integral transforms and their applications

Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.