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Risks
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Applications of Stochastic Optimal Control to Economics and Finance
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Applications of Stochastic Optimal Control to Economics and Finance

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

Deadline for manuscript submissions: closed (31 January 2019) | Viewed by 24448

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Salvatore Federico

E-Mail Website
Guest Editor
Department of Economics and Statistics, University of Siena, Piazza San Francesco 7/8, 53100 Siena, Italy
Interests: stochastic optimal control theory in finite and infinite dimension; problems with delay; stochastic partial differential equations; viscosity solutions of PDEs; singular stochastic control and optimal stopping
Prof. Dr. Giorgio Ferrari

E-Mail Website
Guest Editor
Center for Mathematical Economics, IMW, Bielefeld University, PO Box 10 01 31, 33 501 Bielefeld, Germany
Interests: singular stochastic control; optimal stopping; free-boundary problems; impulse control; stochastic games; real options; mathematical finance; mathematical economics; insurance mathematics
Prof. Dr. Luca Regis

E-Mail Website
Guest Editor
Department of Socio-Economic and Mathematical-Statistical Sciences, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy
Interests: actuarial mathematics; insurance; risk management; longevity risk; asset-liability management; financial mathematics; corporate finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many problems in economics, finance, and actuarial science naturally lead to optimal agents’ dynamic choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and of risk, hedging, optimal timing issues in pricing American options or in investment decisions.

Stochastic control theory provides the methods and results to tackle all such problems, and this Special Issue aims at collecting high quality papers on the theory and application of stochastic optimal control in economics and finance, and its associated computational methods.

Prof. Salvatore Federico
Prof. Giorgio Ferrari
Dr. Luca Regis
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 submissions that pass pre-check are 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 monthly 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 1800 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.

Keywords

  • Individual’s optimal investment/consumption policies;
  • Optimal annuitization;
  • Real options;
  • Optimal timing issues in financial and economic problems;
  • Stochastic games;
  • Pricing and hedging of financial derivatives;
  • Systemic risk;
  • Credit risk;
  • Pension funds management;
  • Theoretical and computational methods in stochastic processes.

Published Papers (7 papers)

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Research

41 pages, 2510 KiB  
Article
Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance
by Jason S. Anquandah and Leonid V. Bogachev
Risks 2019, 7(3), 94; https://doi.org/10.3390/risks7030094 - 01 Sep 2019
Cited by 2 | Viewed by 3872
Abstract
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous [...] Read more.
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous reduction of benefit payments. In the present paper, a simple model of unemployment insurance is proposed with a focus on optimality of the individual’s entry to the scheme. The corresponding optimal stopping problem is solved, and its similarity and differences with the perpetual American call option are discussed. Beyond a purely financial point of view, we argue that in the actuarial context the optimal decisions should take into account other possible preferences through a suitable utility function. Some examples in this direction are worked out. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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20 pages, 871 KiB  
Article
American Options on High Dividend Securities: A Numerical Investigation
by Francesco Rotondi
Risks 2019, 7(2), 59; https://doi.org/10.3390/risks7020059 - 21 May 2019
Viewed by 3071
Abstract
I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an [...] Read more.
I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression is ill-posed, the procedure might deliver biased results. The price of the American option might even fall below the price of its European counterpart. For call options, this is likely to occur when the dividend yield of the underlying is high. This distortion is documented within the standard Black–Scholes–Merton model as well as within its most common extensions (the jump-diffusion, the stochastic volatility and the stochastic interest rates models). Finally, I propose two easy and effective workarounds that fix this distortion. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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23 pages, 1315 KiB  
Article
Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models
by Matteo Brachetta and Claudia Ceci
Risks 2019, 7(2), 48; https://doi.org/10.3390/risks7020048 - 01 May 2019
Cited by 10 | Viewed by 3185
Abstract
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable [...] Read more.
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate r. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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30 pages, 523 KiB  
Article
Imbalance Market Real Options and the Valuation of Storage in Future Energy Systems
by John Moriarty and Jan Palczewski
Risks 2019, 7(2), 39; https://doi.org/10.3390/risks7020039 - 11 Apr 2019
Cited by 1 | Viewed by 2711
Abstract
As decarbonisation progresses and conventional thermal generation gradually gives way to other technologies including intermittent renewables, there is an increasing requirement for system balancing from new and also fast-acting sources such as battery storage. In the deregulated context, this raises questions of market [...] Read more.
As decarbonisation progresses and conventional thermal generation gradually gives way to other technologies including intermittent renewables, there is an increasing requirement for system balancing from new and also fast-acting sources such as battery storage. In the deregulated context, this raises questions of market design and operational optimisation. In this paper, we assess the real option value of an arrangement under which an autonomous energy-limited storage unit sells incremental balancing reserve. The arrangement is akin to a perpetual American swing put option with random refraction times, where a single incremental balancing reserve action is sold at each exercise. The power used is bought in an energy imbalance market (EIM), whose price we take as a general regular one-dimensional diffusion. The storage operator’s strategy and its real option value are derived in this framework by solving the twin timing problems of when to buy power and when to sell reserve. Our results are illustrated with an operational and economic analysis using data from the German Amprion EIM. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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32 pages, 469 KiB  
Article
Optimal Portfolio Selection in an Itô–Markov Additive Market
by Zbigniew Palmowski, Łukasz Stettner and Anna Sulima
Risks 2019, 7(1), 34; https://doi.org/10.3390/risks7010034 - 25 Mar 2019
Cited by 2 | Viewed by 3264
Abstract
We study a portfolio selection problem in a continuous-time Itô–Markov additive market with prices of financial assets described by Markov additive processes that combine Lévy processes and regime switching models. Thus, the model takes into account two sources of risk: the jump diffusion [...] Read more.
We study a portfolio selection problem in a continuous-time Itô–Markov additive market with prices of financial assets described by Markov additive processes that combine Lévy processes and regime switching models. Thus, the model takes into account two sources of risk: the jump diffusion risk and the regime switching risk. For this reason, the market is incomplete. We complete the market by enlarging it with the use of a set of Markovian jump securities, Markovian power-jump securities and impulse regime switching securities. Moreover, we give conditions under which the market is asymptotic-arbitrage-free. We solve the portfolio selection problem in the Itô–Markov additive market for the power utility and the logarithmic utility. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
18 pages, 556 KiB  
Article
Dealing with Drift Uncertainty: A Bayesian Learning Approach
by Carmine De Franco, Johann Nicolle and Huyên Pham
Risks 2019, 7(1), 5; https://doi.org/10.3390/risks7010005 - 09 Jan 2019
Cited by 2 | Viewed by 3761
Abstract
One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated [...] Read more.
One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated with a certain level of confidence, we focus on drift uncertainty in this paper. Building on filtering techniques and learning methods, we use a Bayesian learning approach to solve the Markowitz problem and provide a simple and practical procedure to implement optimal strategy. To illustrate the value added of using the optimal Bayesian learning strategy, we compare it with an optimal nonlearning strategy that keeps the drift constant at all times. In order to emphasize the prevalence of the Bayesian learning strategy above the nonlearning one in different situations, we experiment three different investment universes: indices of various asset classes, currencies and smart beta strategies. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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28 pages, 650 KiB  
Article
On the Failure to Reach the Optimal Government Debt Ceiling
by Abel Cadenillas and Ricardo Huamán-Aguilar
Risks 2018, 6(4), 138; https://doi.org/10.3390/risks6040138 - 04 Dec 2018
Cited by 8 | Viewed by 3585
Abstract
We develop a government debt management model to study the optimal debt ceiling when the ability of the government to generate primary surpluses to reduce the debt ratio is limited. We succeed in finding a solution for the optimal debt ceiling. We study [...] Read more.
We develop a government debt management model to study the optimal debt ceiling when the ability of the government to generate primary surpluses to reduce the debt ratio is limited. We succeed in finding a solution for the optimal debt ceiling. We study the conditions under which a country is not able to reduce its debt ratio to reach its optimal debt ceiling, even in the long run. In addition, this model with bounded intervention is consistent with the fact that, in reality, countries that succeed in reducing their debt ratio do not do so immediately, but over some period of time. To the best of our knowledge, this is the first theoretical model on the debt ceiling that accounts for bounded interventions. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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