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Olena Ragulina - One of the best experts on this subject based on the ideXlab platform.

  • risk model with variable Premium Intensity and investments in one risky asset
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where Premium Intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion. Our main aim is to show that if the Premium Intensity grows rapidly with increasing surplus, then an upper exponential bound for the ruin probability holds under certain conditions in spite of the fact that all surplus is invested in the risky asset. To this end, we apply the supermartingale approach and allow the surplus process to explode. To be more precise, we let the Premium Intensity be a quadratic function. In addition, we investigate the question concerning the probability of explosion of the surplus process between claim arrivals in detail.

  • risk model with variable Premium Intensity and investments in one risk free and a few risky assets
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where a Premium Intensity depends on a current surplus of an insurance company. The surplus is invested in one risk-free and a few risky assets. In addition, borrowing is also possible. The prices of the risky assets follow geometric Brownian motions, which are not necessarily independent. Our main aim is to obtain an upper exponential bound for the ruin probability under some constant investment strategy. To this end, we establish the supermartingale property for an auxiliary exponential process. Finally, we deal with exponentially distributed claim sizes and constant Premium Intensity. For this case, we consider some examples and compare results obtained.

  • risk model with variable Premium Intensity and investments in one risky asset up to the stopping time of investment activity
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where a Premium Intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion, but an insurance company stops its investment activity when the price of the risky asset goes down below some fixed level. Our main result asserts that an upper exponential bound for the ruin probability holds under certain conditions. To this end, we give another representation for the surplus process, redefine the ruin time and establish the supermartingale property for an auxiliary exponential process. Then, we concentrate on the case of exponentially distributed claim sizes. Moreover, we consider the modification of the model where the insurance company stops its investment activity when the price of the risky asset exits from some fixed interval and extend the results obtained to this modification.

  • ruin probability in a risk model with variable Premium Intensity and risky investments
    Opuscula Mathematica, 2015
    Co-Authors: Yuliya Mishura, Mykola Perestyuk, Olena Ragulina
    Abstract:

    We consider a generalization of the classical risk model when the Premium Intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.

Yuliya Mishura - One of the best experts on this subject based on the ideXlab platform.

  • risk model with variable Premium Intensity and investments in one risky asset
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where Premium Intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion. Our main aim is to show that if the Premium Intensity grows rapidly with increasing surplus, then an upper exponential bound for the ruin probability holds under certain conditions in spite of the fact that all surplus is invested in the risky asset. To this end, we apply the supermartingale approach and allow the surplus process to explode. To be more precise, we let the Premium Intensity be a quadratic function. In addition, we investigate the question concerning the probability of explosion of the surplus process between claim arrivals in detail.

  • risk model with variable Premium Intensity and investments in one risk free and a few risky assets
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where a Premium Intensity depends on a current surplus of an insurance company. The surplus is invested in one risk-free and a few risky assets. In addition, borrowing is also possible. The prices of the risky assets follow geometric Brownian motions, which are not necessarily independent. Our main aim is to obtain an upper exponential bound for the ruin probability under some constant investment strategy. To this end, we establish the supermartingale property for an auxiliary exponential process. Finally, we deal with exponentially distributed claim sizes and constant Premium Intensity. For this case, we consider some examples and compare results obtained.

  • risk model with variable Premium Intensity and investments in one risky asset up to the stopping time of investment activity
    Ruin Probabilities#R##N#Smoothness Bounds Supermartingale Approach, 2017
    Co-Authors: Yuliya Mishura, Olena Ragulina
    Abstract:

    In this chapter, we consider a generalization of the classical risk model where a Premium Intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion, but an insurance company stops its investment activity when the price of the risky asset goes down below some fixed level. Our main result asserts that an upper exponential bound for the ruin probability holds under certain conditions. To this end, we give another representation for the surplus process, redefine the ruin time and establish the supermartingale property for an auxiliary exponential process. Then, we concentrate on the case of exponentially distributed claim sizes. Moreover, we consider the modification of the model where the insurance company stops its investment activity when the price of the risky asset exits from some fixed interval and extend the results obtained to this modification.

  • ruin probability in a risk model with variable Premium Intensity and risky investments
    Opuscula Mathematica, 2015
    Co-Authors: Yuliya Mishura, Mykola Perestyuk, Olena Ragulina
    Abstract:

    We consider a generalization of the classical risk model when the Premium Intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.

Mykola Perestyuk - One of the best experts on this subject based on the ideXlab platform.

Čegytė Almina - One of the best experts on this subject based on the ideXlab platform.

  • Ruin probability for inhomogeneous compound discrete-time renewal risk model
    Institutional Repository of Vilnius University, 2016
    Co-Authors: Čegytė Almina
    Abstract:

    In the beginning of the master thesis, the conditions are considered under which distribution of random sum ξ1+ξ2+. . .+ξη belongs to the class L intersection with D. Here {ξ1, ξ2, . . .} is a sequence of independent but not necessarily identically distributed non-negative random variables (r.v), while η is non-negative, non-degenerate at zero, integer valued and independent of {ξ1, ξ2, . . .} r.v. In the second part of the thesis, after all necessary conditions are analyzed, the asymptotic formula is considered for the finite time ruin probability for Inhomogeneous Compound Discrete-Time Renewal Risk model. Such model is defined by the formula: ˆU(t) = u + ct –sum_{k=1}to{t}sum_{i=1}to{η_k}(ξi )^(k), t in N where u >= 0 is initial risk reserve, o c > 0 Premium Intensity. A sequence of r.v. {(ξ1)^(k), (ξ2)^(k), . . .}k=1 to infinity describes claims sizes at moment k. We suppose that {(ξ1)^(k), (ξ2)^(k), . . .}k=1 to infinity are copies of independent sequence of r.v. {ξ1, ξ2, . . .} with distribution functions {F 1 , F 2 , . . .}. Non-negative, non-degenerate at zero and integer-valued r.v. η_k is the number of claims within time interval (k − 1, k] with distribution function Fη. In addition, we suppose that r.v. η1, η2, . . . and (ξ1)^(1) , (ξ2)^(1), . . . , (ξ1)^(2) , (ξ2)^(2),. . . are independent. Finally, we apply obtained asymptotic formula for more specific risk renewal model, where r.v. η has a bounded support and F_ξi belong to class L intersection with D for each i = 1, 2, . .