Publications: Actuarial Science & Mathematical Finance

2020-21


 

A new class of severity regression models with an application to IBNR prediction

by Fung, T.C., Badescu, A., and Lin, X.S.

North American Actuarial Journal | 2021 (forthcoming)

Short Summary: This paper proposes a transformed Gamma logit-weighted mixture of experts (TG-LRMoE) model for severity regression.

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Cascade Sensitivity Measures

by Silvana Pesenti, Pietro Millossovich, and Andreas Tsanakas

Risk Analysis | 2021 (accepted)

Short Summary: In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed \textit{cascade sensitivity}, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus explicitly capturing the direct impact of the stressed input factor, as well as indirect effects via other inputs. Furthermore, alternative representations of the cascade sensitivity measure are derived, allowing us to address practical issues, such as incomplete specification of the model and high computational costs. The applicability of the methodology is illustrated through the analysis of a commercially used insurance risk model.

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Conditional Optimal Stopping: A Time-Inconsistent Optimization

by Marcel Nutz, and Yuchong Zhang

Annals of Applied Probability | 2020 | 30(4), 1669-1692

Short Summary: Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time of stopping, or a company may condition on not being bankrupt. We observe that conditional optimization is time-inconsistent due to the dynamic change of the conditioning probability and develop an equilibrium approach in the spirit of R. H. Strotz’ work for sophisticated agents in discrete time. Equilibria are found to be essentially unique in the case of a finite time horizon whereas an infinite horizon gives rise to nonuniqueness and other interesting phenomena. We also introduce a theory which generalizes the classical Snell envelope approach for optimal stopping by considering a pair of processes with Snell-type properties.

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Efficient dynamic hedging for large variable annuity portfolios with multiple underlying assets

by Lin, X.S. and Yang, S.

ASTIN Bulletin, The Journal of the IAA | 2020 | 50(3), 913-957

Short Summary: In this paper, we extend the surrogate model-assisted nest simulation approach in Lin and Yang [(2020) to efficiently calculate the total VA liability and the partial dollar Deltas for large VA portfolios with multiple underlying assets, and to perform dynamic hedging and profit and loss (P&L) analysis for the portfolio.

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Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach

by Lin, X.S. and Yang, S.

Insurance: Mathematics and Economics | 2020 | 91, 85-103

Short Summary: The nested-simulation is commonly used for calculating the predictive distribution of the total variable annuity (VA) liabilities of large VA portfolios. Due to the large numbers of policies, inner-loops and outer-loops, running the nested-simulation for a large VA portfolio is extremely time consuming and often prohibitive. In this paper, the use of surrogate models is incorporated into the nested-simulation algorithm so that the nested-simulation algorithm can be run much efficiently. The algorithm enables to accurately approximate the predictive distribution of the total VA liability at a significantly reduced running time.

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Fitting multivariate Erlang mixtures to data: A roughness penalty approach

by Wenyong Gui, Rongtan Huang, and X Sheldon Lin

Journal of Computational and Applied Mathematics | 2021(accepted)

Short Summary: In this paper, we propose a generalized expectation conditional maximization (GECM) algorithm that maximizes a penalized likelihood with a proposed roughness penalty.

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LRMoE.jl: a software package for flexible actuarial loss modelling using mixture of experts regression model

by Tseung, S.C, Badescu, A., Fung, T.C., and Lin, X.S.

Annals of Actuarial Science | 2021 (forthcoming)

Short Summary: This paper introduces a new julia package, LRMoE, a statistical software tailor-made for actuarial applications which allows actuarial researchers and practitioners to model and analyze insurance loss frequencies and severities using the Logit-weighted Reduced Mixture-of-Experts (LRMoE) model.

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Scenario Weights for Importance Measurement (SWIM) – an R package for sensitivity analysis

by Silvana Pesenti, Alberto Bettini, Pietro Millossovich, and Andreas Tsanakas

Annals of Actuarial Science | 2021 | 1/26/2021

Short Summary: The SWIM package implements a flexible sensitivity analysis framework, based primarily on results and tools developed by Pesenti et al. (2019). SWIM provides a stressed version of a stochastic model, subject to model components (random variables) fulfilling given probabilistic constraints (stresses). Possible stresses can be applied on moments, probabilities of given events, and risk measures such as Value-at-Risk and Expected Shortfall. SWIM operates upon a single set of simulated scenarios from a stochastic model, returning scenario weights, which encode the required stress and allow monitoring the impact of the stress on all model components. The scenario weights are calculated to minimise the relative entropy with respect to the baseline model, subject to the stress applied. As well as calculating scenario weights, the package provides tools for the analysis of stressed models, including plotting facilities and evaluation of sensitivity measures. SWIM does not require additional evaluations of the simulation model or explicit knowledge of its underlying statistical and functional relations; hence it is suitable for the analysis of black box models. The capabilities of SWIM are demonstrated through a case study of a credit portfolio model.

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Terminal Ranking Games

by Erhan Bayraktar, and Yuchong Zhang

Mathematics of Operations Research | 2021 | Ahead of Print

Short Summary: We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrödinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players’ welfare as well as calculate the price of anarchy.

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Time-consistent conditional expectation under probability distortion

by Jin Ma, Ting-Kam Leonard Wong, and Jianfeng Zhang

Mathematics of Operations Research | 2021

Short Summary: When the underlying probability distorted by a weighting function, we construct a nonlinear conditional expectation such that the tower property remains valid. This construction is of interest in time-inconsistent stochastic optimization problem.

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Previous Publications

Algorithmic Trading, Stochastic Control, and Mutually Exciting Processes

by Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci

SIAM Review | 2018 | Issue: 60(3), 673–703

Short Summary: On electronic exchanges, orders tend to induce cross-excitation in market activity, e.g., when a buy order arrives it may induce increased activity of both buy and sell orders and induce changes in the limit order book. This paper develops a detailed model of this phonomena, and takes a mathematical look at the resulting optimal control problem.

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An IBNR-RBNS insurance risk model with marked Poisson arrivals

by Ahn S., Badescu A., Cheung E., Kim Y.

Insurance: Mathematics and Economics | 2018 | Issue: 79, 26-42

Short Summary: A connection between Mathematical Risk Theory and Stochastic Claim Reserving

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Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio

by Christa Cuchiero, Walter Schachermayer and Ting-Kam Leonard Wong

Mathematical Finance | 2018

Short Summary: We study Cover's universal portfolio in the context of stochastic portfolio theory, where the market portfolio is the numeraire. Under suitable conditions, we prove that the universal portfolio is asymptotically optimal.

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Exponentially concave functions and a new information geometry

by Soumik Pal and Ting-Kam Leonard Wong

Annals of Probability | Volume 46, Number 2 (2018), 1070-1113

Short Summary: This paper uncovers deep connections between optimal transport and information geometry. It develops the dual geometry of L-divergence which extends the classical Bregman divergence. Our geometry can be applied to determine the optimal rebalancing frequency of portfolios.

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Trading Algorithms with Learning in Latent Alpha Models Mathematical Finance 

by Philippe Casgrain and Sebastian Jaimungal

Mathematical Finance | 2018

Short Summary: How does one trade when markets are driven by factors you cannot observe? This paper formulates the problem as a partial information stochastic control problem, proves various theoretical results related to the problem, solves it, uses machine learning techniques to estimate model parameters, and runs simulations to illustrate the results.

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