First Passage Problems in Finance and Insurance

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

Deadline for manuscript submissions: closed (20 February 2023) | Viewed by 2274

Special Issue Editor


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Guest Editor
School of Mathematics and Statistics, Victoria University of Wellington, Gate 6 Kelburn PDE, Wellington 6140, New Zealand
Interests: actuarial science; financial stochastics; optimal capital structure; optimal portfolio; optimal stopping and free-boundary problem of Levy process; applied probability and stochastic modeling; statistical inference for a finite general mixture; regime switching of Markov jump processes
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Special Issue Information

Dear Colleagues,

In a variety of applications in finance and insurance, most temporal risk-and-return optimization problems may be formulated in terms of optimal stopping problems for a given trading strategy of an investor and the underlying financial asset price process. Depending on the nature of the problem, it may be reduced to finding a critical value (optimal stopping boundary) of the underlying asset price beyond which it is optimal to exercise the trading strategy at the first instance that the asset price process crosses the boundary. This is a first passage problem, which has attracted considerable attention over the years since the seminal work of D. A. Darling and A. J. F. Siegert (Annals of Mathematical Statistics, 24(4), p. 624-639, 1953). Recent developments in modern probability theory allow one to obtain analytical solutions or approximate solutions to some first passage problems.

In this Special Issue, entitled “First Passage Problems in Finance and Insurance”, I would like to invite you to submit your latest research paper for publication in the “Risks” journal. This Issue will provide an outlet for researchers to present up-to-date mathematical methods and applications in finance and insurance. High-quality research papers in areas related to first passage problems are welcome. Papers may address theoretical, numerical or practical issues in these areas.

Dr. Budhi Surya
Guest Editor

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.

Published Papers (1 paper)

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Research

17 pages, 447 KiB  
Article
How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability
by Jing Wang, Zbigniew Palmowski and Corina Constantinescu
Risks 2021, 9(9), 157; https://doi.org/10.3390/risks9090157 - 26 Aug 2021
Viewed by 1536
Abstract
In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear ordinary [...] Read more.
In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear ordinary differential equations, we derive the asymptotics of the ruin probabilities when the initial reserve tends to infinity. When considering premiums that are linearly dependent on reserves, representing, for instance, returns on risk-free investments of the insurance capital, we firstly derive explicit solutions of the ordinary differential equations under considerations, in terms of special mathematical functions and integrals, from which we can further determine their asymptotics. This allows us to recover the ruin probabilities obtained for general premiums dependent on reserves. We compare them with the asymptotics of the equivalent ruin probabilities when the premium rate is fixed over time, to measure the gain generated by this additional mechanism of binding the premium rates with the amount of reserve owned by the insurance company. Full article
(This article belongs to the Special Issue First Passage Problems in Finance and Insurance)
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