Special Issue "Recent Advances in Mathematical Modeling of the Financial Markets"

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (15 June 2015)

Special Issue Editors

Guest Editor
Prof. Dr. Emiliano A. Valdez

Department of Mathematics, University of Connecticut, Storrs, CT, USA
Website | E-Mail
Interests: copula models and dependencies; elliptical distributions and their applications; managing post- retirement assets; longevity risks and annuitization; risk measures and capital requirements; applications of financial economics in actuarial science; competing risks models; survival analysis
Guest Editor
Dr. Albert Cohen

Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
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Interests: Financial mathematics; financial markets; actuarial science; insurance; financial risk management
Guest Editor
Dr. Nick Costanzino

RiskLab, University of Toronto, Toronto, ON M5S 3G3, Canada
E-Mail
Interests: Financial mathematics; financial markets; actuarial science; insurance; financial risk management

Special Issue Information

Dear Colleagues,

Michigan State University (MSU) will host the Central Spring meeting of the American Mathematical Society (AMS) on March 14–15, 2015 (Saturday–Sunday). It will be held on the campus of MSU, situated in East Lansing, Michigan, USA. The program consists of Invited Addresses, Special Sessions, and Contributed Paper Sessions. At the meeting, a Special Session on "Recent Advances in Mathematical Modeling of the Financial Markets" has been approved to be organized by Prof. Dr. Emiliano A. Valdez and Dr. Albert Cohen of the MSU Department of Mathematics and Dr. Nick Costanzino of RiskLab Toronto (http://www.ams.org/meetings/sectional/2229_program_ss32.html#title).

This special session is all about modeling of the financial markets, a highly interdisciplinary field that requires the skills of experienced practitioners and academics from mathematics, insurance, and finance. This session will allow for speakers to lecture on topics such as (but not limited to) dealing with regulators and implementing their recommendations, pricing of products that link insurance and finance, measuring and managing counterparty risk, modeling recovery processes, and the modeling of new financial products that are based on credit quality, equities, and bonds. We expect the industrial and academic speakers to talk about their current practice and research. The organizers will also ensure that a review session is held to bring interested mathematicians new to the field up to speed on the basics tools needed to begin a fruitful line of research.

Only invited speakers may participate on this special session and those invited are highly encouraged to submit a paper version of their presentations to be published in this Special Issue of Risks. Co-authors of work presented at the session may submit for publication, and, in special cases, the Guest Editors may also solicit outstanding work closely related to the session for consideration for publication in this Special Issue.

The AMS, which was founded in 1888, and later incorporated in 1923, aims to "further the interests of mathematical research and scholarship" through publications, meetings, conferences, and many other sponsored programs. AMS membership today includes about 30,000 individuals and 580 institutions in the US and around the globe. Previous sectional meetings have been held throughout each year at places like Texas Tech University, University of Colorado, Iowa State University, and Cornell University.

Special Session on “Recent Advances in Mathematical Modeling of the Financial Markets”

http://www.ams.org/meetings/sectional/2229_program_ss32.html#title

Prof. Dr. Emiliano A. Valdez
Dr. Albert Cohen
Dr. Nick Costanzino
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (4 papers)

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Research

Open AccessArticle Stochastic Optimal Control for Online Seller under Reputational Mechanisms
Risks 2015, 3(4), 553-572; doi:10.3390/risks3040553
Received: 28 August 2015 / Accepted: 25 November 2015 / Published: 4 December 2015
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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
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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)
Open AccessFeature PaperArticle Production Flexibility and Hedging
Risks 2015, 3(4), 543-552; doi:10.3390/risks3040543
Received: 18 July 2015 / Accepted: 25 November 2015 / Published: 4 December 2015
Cited by 1 | PDF Full-text (276 KB) | HTML Full-text | XML Full-text
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
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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)
Open AccessArticle Hidden Markov Model for Stock Selection
Risks 2015, 3(4), 455-473; doi:10.3390/risks3040455
Received: 16 June 2015 / Accepted: 23 October 2015 / Published: 29 October 2015
Cited by 1 | PDF Full-text (320 KB) | HTML Full-text | XML Full-text
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
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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)
Figures

Open AccessArticle Options with Extreme Strikes
Risks 2015, 3(3), 234-249; doi:10.3390/risks3030234
Received: 17 May 2015 / Accepted: 4 July 2015 / Published: 8 July 2015
Cited by 1 | PDF Full-text (334 KB) | HTML Full-text | XML Full-text
Abstract
In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black–Scholes models. We analyze European, Asian, American, Parisian and perpetual
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In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black–Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the tail asymptotics for these option types fall into four scenarios. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of the Financial Markets)
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