Department of

Mathematics


Seminar Calendar
for Actuarial Science and Financial Mathematics events the year of Thursday, November 23, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, September 6, 2017

3:00 pm in 345 Altgeld Hall,Wednesday, September 6, 2017

Modeling Dependent Insurance Risks: Customer Loyalty and Risk in Personal Insurance

Edward W. Frees (University of Wisconsin-Madison, Risk and Insurance)

Abstract: In the first portion of the talk I discuss the importance of modeling dependencies among insurance risks. I set the stage for this by describing various risk control mechanisms that the insurer has at its disposal and use this platform for describing the types of associations that are of concern to insurers. To model dependencies, I focus on the use of a copula, a probabilistic tool widely used in insurance and other disciplines. The second portion of the talk, on "Customer Loyalty and Risk in Personal Insurance," is joint work with Catalina Bolancé, Montserrat Guillén, and Emiliano Valdez. This work connects two strands of research on modeling personal (automobile and homeowners) insurance. One strand involves understanding the joint outcomes of separate personal insurance contracts, e.g., do higher automobile claims suggest more severe homeowner claims? A second strand of the literature involves understanding determinants of customer loyalty. For example, we now know that when a customer cancels one insurance contract, he or she is likely to cancel all other contracts soon after. We use copula regression to model the joint outcomes of auto and home claims as well as customer loyalty. Including customer loyalty, or duration with the company, is complicated because of the censoring of this time variable as well as the discreteness. Although customers may cancel the contract at any time, cancellation typically occurs at contract renewal, making this variable essentially a discrete outcome. Composite likelihood and generalized method of moments techniques allow us to address the special features of this data structure.

Tuesday, September 12, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, September 12, 2017

Asymptotic theory of parametric inference for ruin probability under Levy insurance risks

Yasutaka Shimizu (Department of Applied Mathematics, Waseda University)

Abstract: The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a Levy process. Assuming a parametric family for the Levy measures, we estimate the parameter from the surplus data, and estimate the ruin probability via the "delta method". However the asymptotic variance includes the derivative of the ruin probability with respect to the parameter, which is not generally given explicitly, and the confidence interval is not straightforward even if the ruin probability is well estimated. This paper gives the Cramer-type approximation for the derivative, and gives an asymptotic confidence interval of ruin probability.

Tuesday, October 3, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, October 3, 2017

Valuation of Large Variable Annuity Portfolios: Challenges and Potential Solutions

Guojin Gan (Department of Mathematics, University of Connecticut)

Abstract: In the past two decades, lots of variable annuity contracts have been sold by insurance companies. Insurers with large blocks of variable annuity business have faced great challenges especially when it comes to valuing the complex guarantees embedded in these products. The financial risks associated with guarantees embedded in variable annuities cannot be adequately addressed by traditional actuarial approaches. In practice, dynamic hedging is usually adopted by insurers and the hedging is done on the whole portfolio of VA contracts. Since the guarantees embedded in VA contracts sold by insurance companies are complex, insurers resort to Monte Carlo simulation to calculate the Greeks required by dynamic hedging but this method is extremely time-consuming when applied to a large portfolio of VA contracts. In this talk, I will talk about two major computational problems associated with dynamic hedging and present some potential solutions based on statistical learning to address these computational problems.

Tuesday, November 7, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, November 7, 2017

An Extreme Value Approach to the Pricing and Basis Risk Characterization of ILS

Zhongyi Yuan (Pennsylvania State University Smeal College of Business)

Abstract: Insurance-Linked Securities (ILS) as a channel to transfer catastrophe risks to the capital market have been widely used by insurers to enhance their risk bearing capacity. They have developed from covering one single area/peril to multiple, and in the meantime, while traditional ILS are typically linked to natural catastrophe risks only, recent innovations have introduced ILS that are also linked to broader financial risks. We propose a general pricing framework with a pricing measure that combines a risk-neutral measure, which prices the financial risks, and a distorted measure, which prices the natural catastrophe risks. We then use Catastrophe (CAT) bonds as an example to discuss their pricing. Furthermore, since the hedging by ILS may not be a perfect one for insurers, we propose two models to characterize the hedging basis risk, using dual-triggered Industry Loss Warranties (ILW) as an example. In our analysis we employ an extreme value approach to approximate the distribution of the ILS triggers. Finally, we show a few numerical examples to illustrate the results.

Tuesday, November 28, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, November 28, 2017

Pareto Optimality and Robust Optimisation

Vali Asimit (Cass Business School, London, UK)

Abstract: The optimal reinsurance contract has been a topic of great interest for many decades in the insurance literature. The primary insurer aims to share the risk with one or many other reinsurers for a premium. Finding the optimal contract has been a topic for a long time in insurance economics literature. Depending on how the problem is put, the solutions are different, but layer reinsurance appears to be optimal contract, which confirms the existing empirical evidence. In this talk, we will focus on finding the optimal contract from the perspective of primary reinsurer or from the perspective of all insurers. Interestingly, all solutions are optimal Pareto when all risk preferences have the translation invariance property. The robustness of the reinsurance contract is also discussed. Finally, we will show that introducing of some constraints, the optimal contract is no longer a layer reinsurance and instead, a proportional reinsurance contract appears to be the optimal one.