Editorial

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Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

by Albert Cohen

Risks 2018, 6(1), 4; https://doi.org/10.3390/risks6010004 - 15 Jan 2018

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In the nearly thirty years since Hans Buhlmann (Buhlmann (1987)) set out the notion of the Actuary of the Third Kind, the connection between Actuarial Science (AS) and Mathematical Finance (MF) has been continually reinforced. As siblings in the family of Risk Management [...] Read more.

In the nearly thirty years since Hans Buhlmann (Buhlmann (1987)) set out the notion of the Actuary of the Third Kind, the connection between Actuarial Science (AS) and Mathematical Finance (MF) has been continually reinforced. As siblings in the family of Risk Management techniques, practitioners in both fields have learned a great deal from each other. The collection of articles in this volume are contributed by scholars who are not only experts in areas of AS and MF, but also those who present diverse perspectives from both industry and academia. Topics from multiple areas, such as Stochastic Modeling, Credit Risk, Monte Carlo Simulation, and Pension Valuation, among others, that were maybe thought to be the domain of one type of risk manager are shown time and again to have deep value to other areas of risk management as well. The articles in this collection, in my opinion, contribute techniques, ideas, and overviews of tools that specialists in both AS and MF will find useful and interesting to implement in their work. It is also my hope that this collection will inspire future collaboration between those who seek an interdisciplinary approach to risk management. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

Research

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1770 KiB

Open AccessFeature PaperArticle

An Analysis and Implementation of the Hidden Markov Model to Technology Stock Prediction

by Nguyet Nguyen

Risks 2017, 5(4), 62; https://doi.org/10.3390/risks5040062 - 24 Nov 2017

Cited by 21 | Viewed by 8912

Abstract

Future stock prices depend on many internal and external factors that are not easy to evaluate. In this paper, we use the Hidden Markov Model, (HMM), to predict a daily stock price of three active trading stocks: Apple, Google, and Facebook, based on [...] Read more.

Future stock prices depend on many internal and external factors that are not easy to evaluate. In this paper, we use the Hidden Markov Model, (HMM), to predict a daily stock price of three active trading stocks: Apple, Google, and Facebook, based on their historical data. We first use the Akaike information criterion (AIC) and Bayesian information criterion (BIC) to choose the numbers of states from HMM. We then use the models to predict close prices of these three stocks using both single observation data and multiple observation data. Finally, we use the predictions as signals for trading these stocks. The criteria tests’ results showed that HMM with two states worked the best among two, three and four states for the three stocks. Our results also demonstrate that the HMM outperformed the naïve method in forecasting stock prices. The results also showed that active traders using HMM got a higher return than using the naïve forecast for Facebook and Google stocks. The stock price prediction method has a significant impact on stock trading and derivative hedging. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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826 KiB

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Bounded Brownian Motion

by Peter Carr

Risks 2017, 5(4), 61; https://doi.org/10.3390/risks5040061 - 17 Nov 2017

Cited by 9 | Viewed by 4142

Abstract

Diffusions are widely used in finance due to their tractability. Driftless diffusions are needed to describe ratios of asset prices under a martingale measure. We provide a simple example of a tractable driftless diffusion which also has a bounded state space. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

2224 KiB

Open AccessArticle

Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

by Gareth W. Peters, Rodrigo S. Targino and Mario V. Wüthrich

Risks 2017, 5(4), 53; https://doi.org/10.3390/risks5040053 - 22 Sep 2017

Cited by 6 | Viewed by 5297

Abstract

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a [...] Read more.

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method to calculate capital allocations for a general insurance company is developed, with a focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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1714 KiB

Open AccessArticle

An Integrated Approach to Pricing Catastrophe Reinsurance

by Carolyn W. Chang and Jack S. K. Chang

Risks 2017, 5(3), 51; https://doi.org/10.3390/risks5030051 - 19 Sep 2017

Cited by 6 | Viewed by 4423

Abstract

We propose an integrated approach straddling the actuarial science and the mathematical finance approaches to pricing a default-risky catastrophe reinsurance contract. We first apply an incomplete-market version of the no-arbitrage martingale pricing paradigm to price the reinsurance contract as a martingale by a [...] Read more.

We propose an integrated approach straddling the actuarial science and the mathematical finance approaches to pricing a default-risky catastrophe reinsurance contract. We first apply an incomplete-market version of the no-arbitrage martingale pricing paradigm to price the reinsurance contract as a martingale by a measure change, then we apply risk loading to price in—as in the traditional actuarial practice—market imperfections, the underwriting cycle, and other idiosyncratic factors identified in the practice and empirical literatures. This integrated approach is theoretically appealing for its merit of factoring risk premiums into the probability measure, and yet practical for being applicable to price a contract not traded on financial markets. We numerically study the catastrophe pricing effects and find that the reinsurance contract is more valuable when the catastrophe is more severe and the reinsurer’s default risk is lower because of a stronger balance sheet. We also find that the price is more sensitive to the severity of catastrophes than to the arrival frequency; implying (re)insurers should focus more on hedging the severity than the arrival frequency in their risk management programs. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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450 KiB

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Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case

by Daoping Yu and Vytaras Brazauskas

Risks 2017, 5(3), 49; https://doi.org/10.3390/risks5030049 - 13 Sep 2017

Cited by 4 | Viewed by 3655

Abstract

Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the “naive” approach, the shifted [...] Read more.

Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the “naive” approach, the shifted approach, and the truncated approach. Since each approach is based on a different set of assumptions, different probability models emerge. Thus, model uncertainty arises. The main objective of this paper is to understand the impact of model uncertainty on the value-at-risk (VaR) estimators. To accomplish that, we take the bank’s perspective and study a single risk. Under this simplified scenario, we can solve the problem analytically (when the underlying distribution is exponential) and show that it uncovers similar patterns among VaR estimates to those based on the simulation approach (when data follow a Lomax distribution). We demonstrate that for a fixed probability distribution, the choice of the truncated approach yields the lowest VaR estimates, which may be viewed as beneficial to the bank, whilst the “naive” and shifted approaches lead to higher estimates of VaR. The advantages and disadvantages of each approach and the probability distributions under study are further investigated using a real data set for legal losses in a business unit (Cruz 2002). Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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Open AccessFeature PaperArticle

Effects of Gainsharing Provisions on the Selection of a Discount Rate for a Defined Benefit Pension Plan

by Robert J. Rietz, Evan Cronick, Shelby Mathers and Matt Pollie

Risks 2017, 5(2), 32; https://doi.org/10.3390/risks5020032 - 20 Jun 2017

Cited by 1 | Viewed by 3608

Abstract

This paper examines the effect of gainsharing provisions on the selection of a discount rate for a defined benefit pension plan. The paper uses a traditional actuarial approach of discounting liabilities using the expected return of the associated pension fund. A stochastic Excel [...] Read more.

This paper examines the effect of gainsharing provisions on the selection of a discount rate for a defined benefit pension plan. The paper uses a traditional actuarial approach of discounting liabilities using the expected return of the associated pension fund. A stochastic Excel model was developed to simulate the effect of varying investment returns on a pension fund with four asset classes. Lognormal distributions were fitted to historical returns of two of the asset classes; large company stocks and long-term government bonds. A third lognormal distribution was designed to represent the investment returns of alternative investments, such as real estate and private equity. The fourth asset class represented short term cash investments and that return was held constant. The following variables were analyzed to determine their relative impact of gainsharing on the selection of a discount rate: hurdle rate, percentage of gainsharing, actuarial asset method smoothing period, and variations in asset allocation. A 50% gainsharing feature can reduce the discount rate for a defined benefit pension plan from 0.5% to more than 2.5%, depending on the gainsharing design and asset allocation. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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2621 KiB

Open AccessFeature PaperArticle

Actuarial Geometry

by Stephen J. Mildenhall

Risks 2017, 5(2), 31; https://doi.org/10.3390/risks5020031 - 16 Jun 2017

Cited by 4 | Viewed by 7442

Abstract

The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This paper [...] Read more.

The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This paper explains why an actuarial analog of the asset volume/return model should be based on a Lévy process. It discusses the impact of different loss models on marginal capital allocations. It shows that Lévy process-based models provide a better fit to the US statutory accounting data, and identifies how parameter risk scales with volume and increases with time. Finally, it shows the data suggest a surprising result regarding the form of insurance parameter risk. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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351 KiB

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Risk Management under Omega Measure

by Michael R. Metel, Traian A. Pirvu and Julian Wong

Risks 2017, 5(2), 27; https://doi.org/10.3390/risks5020027 - 06 May 2017

Cited by 5 | Viewed by 4026

Abstract

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for [...] Read more.

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered, we show that the Omega measure and Sharpe ratio lead to different optimal portfolios. Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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350 KiB

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Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

by Albert Cohen and Nick Costanzino

Risks 2017, 5(2), 26; https://doi.org/10.3390/risks5020026 - 19 Apr 2017

Cited by 6 | Viewed by 5468

Abstract

Building on recent work incorporating recovery risk into structural models by Cohen & Costanzino (2015), we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. [...] Read more.

Building on recent work incorporating recovery risk into structural models by Cohen & Costanzino (2015), we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. This leads to a two-factor structural model we call the Stochastic Recovery Black-Cox model, whereby the asset risk driver A_t defines the default trigger and the recovery risk driver R_t defines the amount recovered in the event of default. We then price zero-coupon bonds and credit default swaps under the Stochastic Recovery Black-Cox model. Finally, we compare our results with the classic Black-Cox model, give explicit expressions for the recovery risk premium in the Stochastic Recovery Black-Cox model, and detail how the introduction of separate but correlated risk drivers leads to a decoupling of the default and recovery risk premiums in the credit spread. We conclude this work by computing the effect of adding coupons that are paid continuously until default, and price perpetual (consol bonds) in our two-factor firm value model, extending calculations in the seminal paper by Leland (1994). Full article

(This article belongs to the Special Issue A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance)

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