arXiv subjects

David Landriault

Publications and source records attributed to David Landriault.

7 recordsLinked to original sources

arXiv2024

Performance-based variable premium scheme and reinsurance design

In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller's risk attitude. Building on the work of Meyers (1980) and Chen et al. (2016), we propose a new performance-based variable premium scheme for reinsurance policies, where the premium depends on both the distribution of the ceded loss and the actual realized loss. Under this scheme, the insurer and the reinsurer face a random premium at the beginning of the policy period. Based on the realized loss, the premium is adjusted into either a ''reward'' or ''penalty'' scenario, resulting in a discount or surcharge at the end of the policy period. We characterize the optimal reinsurance policy from the insurer's perspective under this new variable premium scheme. In addition, we formulate a Bowley optimization problem between the insurer and the monopoly reinsurer. Numerical examples demonstrate that, compared to the expected-value premium principle, the reinsurer prefers the variable premium scheme as it reduces the reinsurer's total risk exposure.

q-fin.RM↗

arXiv2024

Contract Structure and Risk Aversion in Longevity Risk Transfers

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-term protections, the capital market for longevity risk transfer has struggled to gain traction, resulting in only a few short-term instruments. We investigate how differences in risk aversion between the two parties affect the equilibrium structure of longevity risk transfer contracts, contrasting `static' contracts that offer long-term protection with `dynamic' contracts that provide short-term, variable coverage. Our analysis shows that static contracts are preferred by more risk-averse buyers, while dynamic contracts are favored by more risk-averse sellers who are reluctant to commit to long-term agreements. When incorporating information asymmetry through ambiguity, we find that ambiguity can cause more risk-averse sellers to stop offering long-term contracts. With the assumption that global reinsurers, acting as sellers in the reinsurance sector and buyers in the capital market, are generally less risk-averse than other participants, our findings provide theoretical explanations for current market dynamics and suggest that short-term instruments offer valuable initial steps toward developing an efficient and active capital market for longevity risk transfer.

econ.GN↗

arXiv2019

On occupation times in the red of Lévy risk models

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 known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum. By a further Laplace inversion to our results, we obtain the distribution of the occupation time up to a finite time horizon for refracted Brownian motion risk process and refracted Cramér-Lundberg risk model with exponential claims.

q-fin.RM↗

arXiv2017

A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes

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 drawdown (resp. drawup) process, its overshoot, and the maximum of the underlying process at this first passage time. By using short-time pathwise analysis, under some mild regularity conditions, the joint law of the three drawdown quantities is shown to be the unique solution to an integral equation which is expressed in terms of fundamental two-sided exit quantities of the underlying process. Explicit forms for this joint law are found when the Markov process has only one-sided jumps or is a Lévy process (possibly with two-sided jumps). The proposed methodology provides a unified approach to study various drawdown quantities for the general class of time-homogeneous Markov processes.

q-fin.MF↗

arXiv2016

On magnitude, asymptotics and duration of drawdowns for Lévy models

This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy 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 Lévy processes, we derive the law of duration of drawdowns for a large class of Lévy 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 Lévy process.

q-fin.MF↗

arXiv2014

On the Frequency of Drawdowns for Brownian Motion Processes

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 focus on the side of severity by studying the first drawdown over certain pre-specified size. In this paper, we extend the discussion by investigating the frequency of drawdowns, and some of their inherent characteristics. We consider two types of drawdown time sequences depending on whether a historical running maximum {is reset or not}. For each type, we study the frequency rate of drawdowns, the Laplace transform of the $n$-th drawdown time, the distribution of the running maximum and the value process at the $n$-th drawdown time, as well as some other quantities of interest. Interesting relationships between these two drawdown time sequences are also established. Finally, insurance policies protecting against the risk of frequent drawdowns are also proposed and priced.

q-fin.PR↗

arXiv2011

Occupation times of spectrally negative Lévy processes with applications

In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Lévy processes. Our results are extensions of known results for standard Brownian motion and jump-diffusion processes. The results are expressed in terms of the so-called scale functions of the spectrally negative Lévy process and its Laplace exponent. Applications to insurance risk models are also presented.

math.PR↗