Risks

372 KiB

Open AccessArticle

by Michael Merz and Mario V. Wüthrich

Risks 2015, 3(4), 624-646; https://doi.org/10.3390/risks3040624 - 21 Dec 2015

Cited by 2 | Viewed by 5180

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us [...] Read more.

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims prediction and prediction uncertainty for the Munich chain-ladder method in a consistent way. Full article

(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)

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372 KiB

Open AccessArticle

Dependence Uncertainty Bounds for the Expectile of a Portfolio

by Edgars Jakobsons and Steven Vanduffel

Risks 2015, 3(4), 599-623; https://doi.org/10.3390/risks3040599 - 10 Dec 2015

Cited by 9 | Viewed by 4562

Abstract

We study upper and lower bounds on the expectile risk measure of risky portfolios when the joint distribution of the risky components is not fully specified. First, we summarize methods for obtaining bounds when only the marginal distributions of the components are known, [...] Read more.

We study upper and lower bounds on the expectile risk measure of risky portfolios when the joint distribution of the risky components is not fully specified. First, we summarize methods for obtaining bounds when only the marginal distributions of the components are known, but not their interdependence (unconstrained bounds). In particular, we provide the best-possible upper bound and the best-possible lower bound (under some conditions), as well as numerical procedures to compute them. We also derive simple analytic bounds that appear adequate in various situations of interest. Second, we study bounds when some information on interdependence is available (constrained bounds). When the variance of the portfolio is known, a simple-to-compute upper bound is provided, and we illustrate that it may significantly improve the unconstrained upper bound. We also show that the unconstrained lower bound cannot be readily improved using variance information. Next, we derive improved bounds when the bivariate distributions of each of the risky components and a risk factor are known. When the factor induces a positive dependence among the components, it is typically possible to improve the unconstrained lower bound. Finally, the unconstrained dependence uncertainty spreads of expected shortfall, value-at-risk and the expectile are compared. Full article

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353 KiB

Open AccessArticle

Information-Based Trade in German Real Estate and Equity Markets

by Marco Wölfle

Risks 2015, 3(4), 573-598; https://doi.org/10.3390/risks3040573 - 7 Dec 2015

Viewed by 4272

Abstract

This paper employs four established market microstructure measures on information-based trade in financial markets. A set of German mid and small caps is used to analyze potential differential information content in real estate stocks compared to other asset classes. After linking substantially lower [...] Read more.

This paper employs four established market microstructure measures on information-based trade in financial markets. A set of German mid and small caps is used to analyze potential differential information content in real estate stocks compared to other asset classes. After linking substantially lower amounts of information-based trade in real estate stocks to higher liquidity premia, it is found that the evolution of the information content in real estate and other assets follows similar trends. Consequently, interdependence is tested for rolling time windows, revealing strong informational links between real estate and other assets. Particularly, small caps, financials, as well as companies offering consumer goods and services show a close relationship to real estate. Depending on the choice of the measure of information-based trade, up to 75% of the variation in the information content in real estate shares is related to other asset classes, pointing to the notion of high dependence. Full article

(This article belongs to the Special Issue Information and market efficiency)

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1503 KiB

Open AccessArticle

Stochastic Optimal Control for Online Seller under Reputational Mechanisms

by Milan Bradonjić, Matthew Causley and Albert Cohen

Risks 2015, 3(4), 553-572; https://doi.org/10.3390/risks3040553 - 4 Dec 2015

Viewed by 4428

Abstract

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in [...] Read more.

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller’s reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from [1] and used effectively in the Stochastic Optimal Control of Advertising [2]. This model of reputation is combined with the effect of online reputation on sales price empirically verified in [3]. We derive the Hamilton-Jacobi-Bellman (HJB) differential equation, whose solution relates optimal wealth level to a seller’s reputation. We formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of the Financial Markets)

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276 KiB

Open AccessFeature PaperArticle

Production Flexibility and Hedging

by Georges Dionne and Marc Santugini

Risks 2015, 3(4), 543-552; https://doi.org/10.3390/risks3040543 - 4 Dec 2015

Cited by 1 | Viewed by 3815

Abstract

We extend the analysis on hedging with price and output uncertainty by endogenizing the output decision. Specifically, we consider the joint determination of output and hedging in the case of flexibility in production. We show that the risk-averse firm always maintains a short [...] Read more.

We extend the analysis on hedging with price and output uncertainty by endogenizing the output decision. Specifically, we consider the joint determination of output and hedging in the case of flexibility in production. We show that the risk-averse firm always maintains a short position in the futures market when the futures price is actuarially fair. Moreover, in the context of an example, we show that the presence of production flexibility reduces the incentive to hedge for all risk averse agents. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of the Financial Markets)

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620 KiB

Open AccessArticle

The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature

by Alexander Bohnert

Risks 2015, 3(4), 515-542; https://doi.org/10.3390/risks3040515 - 20 Nov 2015

Cited by 1 | Viewed by 5121

Abstract

Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of [...] Read more.

Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of how costly the typical types of guarantees are, in the sense that they reduce a pension saving scheme’s financial performance over time. In this context, we aim to provide a presentation of insights from selected literature studying the impact of point-to-point guarantees and cliquet-style interest rate guarantees on the performance of pension contracts. The comparative analysis emphasizes that, in most cases, guarantee costs are not negligible with regard to a contract’s financial performance, especially compared to benchmarks, and that customers knowingly opt for such guarantees (or not) is, thus, indispensable. To further investigate the willingness-to-pay for guarantees in life insurance is an area for future research, in particular for innovative contract design. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

799 KiB

Open AccessArticle

On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy

by Eric C.K. Cheung, Haibo Liu and Jae-Kyung Woo

Risks 2015, 3(4), 491-514; https://doi.org/10.3390/risks3040491 - 10 Nov 2015

Cited by 12 | Viewed by 5536

Abstract

In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer’s payments to its policyholders and shareholders, respectively. [...] Read more.

In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer’s payments to its policyholders and shareholders, respectively. To this end, we introduce a Gerber–Shiu-type function, which further incorporates the higher moments of these two quantities. This not only unifies the individual study of various ruin-related quantities, but also allows for new measures concerning covariances to be calculated. The integro-differential equation satisfied by the generalized Gerber–Shiu function and the boundary condition are derived. In particular, when the claim severity is distributed as a combination of exponentials, explicit expressions for this Gerber–Shiu function in some special cases are given. Numerical examples involving the covariances between any two of (i) the aggregate discounted claims until ruin, (ii) the discounted dividend payments until ruin and (iii) the time of ruin are presented along with some interpretations. Full article

(This article belongs to the Special Issue Non-Life Insurance Mathematics beyond Risk Theory: Pricing and Claims Reserving)

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313 KiB

Open AccessArticle

Combining Alphas via Bounded Regression

by Zura Kakushadze

Risks 2015, 3(4), 474-490; https://doi.org/10.3390/risks3040474 - 4 Nov 2015

Cited by 3 | Viewed by 5517

Abstract

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then [...] Read more.

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples. Full article

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320 KiB

Open AccessArticle

Hidden Markov Model for Stock Selection

by Nguyet Nguyen and Dung Nguyen

Risks 2015, 3(4), 455-473; https://doi.org/10.3390/risks3040455 - 29 Oct 2015

Cited by 27 | Viewed by 11955

Abstract

The hidden Markov model (HMM) is typically used to predict the hidden regimes of observation data. Therefore, this model finds applications in many different areas, such as speech recognition systems, computational molecular biology and financial market predictions. In this paper, we use HMM [...] Read more.

The hidden Markov model (HMM) is typically used to predict the hidden regimes of observation data. Therefore, this model finds applications in many different areas, such as speech recognition systems, computational molecular biology and financial market predictions. In this paper, we use HMM for stock selection. We first use HMM to make monthly regime predictions for the four macroeconomic variables: inflation (consumer price index (CPI)), industrial production index (INDPRO), stock market index (S&P 500) and market volatility (VIX). At the end of each month, we calibrate HMM’s parameters for each of these economic variables and predict its regimes for the next month. We then look back into historical data to find the time periods for which the four variables had similar regimes with the forecasted regimes. Within those similar periods, we analyze all of the S&P 500 stocks to identify which stock characteristics have been well rewarded during the time periods and assign scores and corresponding weights for each of the stock characteristics. A composite score of each stock is calculated based on the scores and weights of its features. Based on this algorithm, we choose the 50 top ranking stocks to buy. We compare the performances of the portfolio with the benchmark index, S&P 500. With an initial investment of $100 in December 1999, over 15 years, in December 2014, our portfolio had an average gain per annum of 14.9% versus 2.3% for the S&P 500. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of the Financial Markets)

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340 KiB

Open AccessArticle

Risk Classification Efficiency and the Insurance Market Regulation

by Donatella Porrini

Risks 2015, 3(4), 445-454; https://doi.org/10.3390/risks3040445 - 25 Sep 2015

Cited by 14 | Viewed by 6966

Abstract

Given that the insurance market is characterized by asymmetric information, its efficiency has traditionally been based to a large extent on risk classification. In certain regulations, however, we can find restrictions on these differentiations, primarily the ban on those considered to be “discriminatory”. [...] Read more.

Given that the insurance market is characterized by asymmetric information, its efficiency has traditionally been based to a large extent on risk classification. In certain regulations, however, we can find restrictions on these differentiations, primarily the ban on those considered to be “discriminatory”. In 2011, following the European Union Directive 2004/113/EC, the European Court of Justice concluded that any gender-based discrimination was prohibited, meaning that gender equality in the European Union had to be ensured from 21 December 2012. Another restriction was imposed by EU and national competition regulation on the exchange of information considered as anti-competitive behavior. This paper aims to contribute to the recent policy debate in the EU, evaluating the negative economic consequences of these regulatory restrictions in terms of market efficiency. Full article

(This article belongs to the Special Issue Information and market efficiency)

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Risks, Volume 3, Issue 4 (December 2015) – 10 articles , Pages 445-646

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