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Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments

Jing Liu, Huan Zhang
2017 Risks  
As main results, we derive exact asymptotic estimates for the one-year ruin probability for the following cases: (i) X and Y are independent with X of Fréchet type; (ii) X and Y are independent with X  ...  Abstract: Motivated by the EU Solvency II Directive, we study the one-year ruin probability of an insurer who makes investments and hence faces both insurance and financial risks.  ...  Acknowledgments: The authors would like to thank the reviewers for their helpful comments. This research was supported by the National Natural Science Foundation of China (NSFC: 71628104).  ... 
doi:10.3390/risks5020028 fatcat:ev33jg25zrfq5ji6tksfw5bvvm

Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results

Florin Avram, Zbigniew Palmowski, Martijn R. Pistorius
2008 The Annals of Applied Probability  
One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant.  ...  In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cramér light-tail assumption on the claim size distribution.  ...  We are much indebted to an anonymous referee for the careful reading of the manuscript and to Tomasz Rolski for his continuing advice on this paper.  ... 
doi:10.1214/08-aap529 fatcat:32mplpo2gvfftg2xcxxn3xdikq

Tenth conference on stochastic processes and their applications

1982 Stochastic Processes and their Applications  
Shimura, A class of conditional limit theorems related to ruin problems. 2.13. Point processes and geometric probability E. Arias, Estimating dependent life lengths: a point process approach. H.  ...  Ruohonen, Applicability of the corrected diffusion approximation to the problem of ruin in risk processes. 2.3. Queuing theory, Part I A4.I.  ...  We have also compared the ruin in N claims given by the approximation to the exact probability of ruin in time iV. Reference [l] D.  ... 
doi:10.1016/0304-4149(82)90039-4 fatcat:jz2e6rojqngs5bg2ldfptykvp4

Papers from Actuarial Journals Worldwide

2010 Annals of Actuarial Science  
Single copies of all the papers listed here can be obtained, subject to charge and copyright regulations, from the actuarial profession's libraries. Issues may be borrowed by members.  ...  the asymptotic distribution of the time to ruin and the amount of dividends paid until ruin.  ...  We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model.  ... 
doi:10.1017/s1748499510000084 fatcat:pqk7gmcyq5gjzlh3ozvgd4x7na

The Mathematics and Statistics of Quantitative Risk Management

Thomas Mikosch, Paul Embrechts, Richard Davis
2008 Oberwolfach Reports  
The main objective was to account for the state of the art of statistical and probabilistic modeling in risk management and, in particular, to collect problems which need an urgent theoretical solution  ...  rates, foreign exchange rates, etc.) or by difference equations for time series.  ...  We show that the ruin problem corresponds to determining hitting probabilities for the solution to a random perturbation of a stochastic integral equation.  ... 
doi:10.4171/owr/2008/15 fatcat:arq57nwp5rhipoomndr4b2mvhe

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2014 Annals of Actuarial Science  
As applications, we consider a discrete-time risk model with dependent insurance and financial risks, and obtain the asymptotic behavior for the (in)finite-time ruin probabilities.  ...  Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression.  ... 
doi:10.1017/s1748499514000207 fatcat:w6qlf5k6mjfo7pwqhjtoj4ufpy

Lundberg's risk process with tax

Hansjörg Albrecher, Christian Hipp
2007 Blätter der DGVFM  
For numerical purposes, when the evaluation of the exact solution (9) is not feasible, it may be helpful to start directly from the above differential equation.  ...  The absence of the inhomogeneous term in (6) causes the problem not to rule out the solution φ γ (s) = 0 (as discussed in the Remark after Theorem 1).  ...  It is shown that the resulting survival probability is a power of the survival probability without tax.  ... 
doi:10.1007/s11857-007-0004-4 fatcat:vnt5o2o6eraqxboxbu64nzau4e

Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model [article]

Michael Preischl, Stefan Thonhauser
2018 arXiv   pre-print
We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.  ...  Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton-Jacobi-Bellman equation  ...  So only the constant C δ,w depends on the penalty function w, while the asymptotic behaviour is governed by the adjustment coefficient just as in the case of the discounted ruin probability.  ... 
arXiv:1809.00990v1 fatcat:3eoeyorypjgx7j3sfre2z6s5oa

Lévy insurance risk process with Poissonian taxation

Zhimin Zhang, Eric C.K. Cheung, Hailiang Yang
2015 Scandinavian Actuarial Journal  
event of ruin is checked and tax may be collected from the tax authority.  ...  The Cramér-Lundberg asymptotic formula is shown to hold true for the Gerber-Shiu function, and it differs from the case without tax by a multiplicative constant.  ...  Acknowledgements The authors would like to thank the anonymous referee(s) for helpful comments and suggestions which improved an earlier version of the paper.  ... 
doi:10.1080/03461238.2015.1062042 fatcat:tzuuwqkjzrbuvmzsryk3qct52i

Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model

Krzysztof Dȩbicki, Lanpeng Ji, Tomasz Rolski
2019 Risks  
We study the ruin function P ( u ) for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where u is the same initial capital for each line.  ...  We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of - ln P ( u ) / u as u tends to infinity, which depends essentially on the correlation ρ of the two  ...  An open and difficult problem is the derivation of exact asymptotics for P(u) in (4), for which the problem of finding dominating points would be the first step.  ... 
doi:10.3390/risks7030083 fatcat:yokq2wnr7zajbmaqgi76ue7akq

Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model

Franck Adékambi, Kokou Essiomle
2021 Risks  
by using a general dependence structure between the inter-occurrence time and the claim sizes.  ...  This dependence structure is relevant since it is well known that under catastrophic or extreme events the inter-occurrence time and the claim severities are dependent.  ...  Acknowledgments: The authors would like to thank the editor and four anonymous referees for many constructive comments which greatly helped to improve the quality of this paper.  ... 
doi:10.3390/risks9070122 fatcat:tgofzoxr25hcrkp6zxsiagvcei

Resolving phase transitions with Discontinuous Galerkin methods [article]

Eduardo Grossi, Nicolas Wink
2019 arXiv   pre-print
We discuss results for the Riemann problem, as well as initial conditions leading to a first and second order phase transition.  ...  We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (FRG).  ...  Hereby we assume the result obtained via the method of characteristics to be the exact solution. As explained in Section II B, we use an implicit solver for the time evolution.  ... 
arXiv:1903.09503v3 fatcat:w6svnqmxqzg3vaosqbnbzy7f2i

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin
2012 Computational Mathematics and Mathematical Physics  
of the solution are given, and an algorithm for its numerical determination is described.  ...  value problem with constraints; related singular boundary value problems for ordinary differential equations; existence, uniqueness, and behavior of a solution; numerical solution algorithm.  ...  ACKNOWLEDGMENTS The authors are grateful to A.A. Abramov for discussing this work. This work was supported by the Russian Foundation for Basic Research, project nos. 10 01 00767 a and 11 01 00219 a.  ... 
doi:10.1134/s0965542512100077 fatcat:sjpy53ybffc7tp2o2zghe7tk4u

A Study of Policy Gradient on a Class of Exactly Solvable Models [article]

Gavin McCracken, Colin Daniels, Rosie Zhao, Anna Brandenberger, Prakash Panangaden, Doina Precup
2020 arXiv   pre-print
of this problem.  ...  In this paper, we explore the evolution of the policy parameters, for a special class of exactly solvable POMDPs, as a continuous-state Markov chain, whose transition probabilities are determined by the  ...  Acknowledgements We thank Luc Devroye for assisting us with the literature review on path counting as well as putting up with regular invasions of his office. References  ... 
arXiv:2011.01859v1 fatcat:qqvqwge6q5garbivqrshqcmwp4

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2015 Annals of Actuarial Science  
for the finite-time ruin probability an explicit asymptotic formula.  ...  Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims. 185-192.  ... 
doi:10.1017/s1748499514000323 fatcat:abz3p5cghvgmxhylgtxxfg5s6i
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