scholarly journals Squared Bessel process with delay

2016 ◽  
pp. 199-206
Author(s):  
Lochana Siriwardena ◽  
Harry Hughes
Keyword(s):  
Bessel Process ◽  
Squared Bessel Process

Invariance formulas for stopping times of squared Bessel process

2018 ◽  
Vol 36 (4) ◽  
pp. 671-699
Author(s):  
Jacek Jakubowski ◽  
Maciej Wiśniewolski
Keyword(s):  
Bessel Process ◽  
Stopping Times ◽  
Squared Bessel Process

scholarly journals LESS-EXPENSIVE VALUATION AND RESERVING OF LONG-DATED VARIABLE ANNUITIES WHEN INTEREST RATES AND MORTALITY RATES ARE STOCHASTIC

2020 ◽  
Vol 50 (2) ◽  
pp. 381-417
Author(s):  
Kevin Fergusson
Keyword(s):  
Interest Rates ◽  
Mortality Rates ◽  
Bessel Process ◽  
Insurance Markets ◽  
Rate Model ◽  
Ancillary Benefits ◽  
Variable Annuities ◽  
Mortality Model ◽  
Squared Bessel Process ◽  
Benchmark Approach

AbstractVariable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

scholarly journals Asymptotic behavior of critical, irreducible multi-type continuous state and continuous time branching processes with immigration

2016 ◽  
Vol 16 (04) ◽  
pp. 1650008 ◽  
Author(s):  
Mátyás Barczy ◽  
Gyula Pap
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Branching Processes ◽  
Bessel Process ◽  
Step Functions ◽  
Squared Bessel Process ◽  
Continuous State ◽  
Random Step ◽  
Branching Process With Immigration ◽  
Continuous Time Branching Processes

Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of appropriately scaled random step functions formed from a critical, irreducible multi-type continuous state and continuous time branching process with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of a matrix related to the branching mechanism of the branching process in question.

A note on switching property for squared Bessel process

2020 ◽  
Vol 60 (4) ◽  
pp. 482-493
Author(s):  
Jacek Jakubowski ◽  
Maciej Wiśniewolski
Keyword(s):  
Bessel Process ◽  
Squared Bessel Process ◽  
Switching Property

A boundary crossing probability for the Bessel process

1998 ◽  
Vol 30 (3) ◽  
pp. 807-830 ◽  
Author(s):  
Rebecca A. Betensky
Keyword(s):  
Nonparametric Test ◽  
Bessel Process ◽  
Boundary Crossing ◽  
Test Statistic ◽  
Boundary Crossing Probability ◽  
Significance Level ◽  
Straight Line ◽  
Crossing Probability ◽  
Nonparametric Test Statistic ◽  
First Crossing Time

Analytic approximations are derived for the distribution of the first crossing time of a straight-line boundary by a d-dimensional Bessel process and its discrete time analogue. The main ingredient for the approximations is the conditional probability that the process crossed the boundary before time m, given its location beneath the boundary at time m. The boundary crossing probability is of interest as the significance level and power of a sequential test comparing d+1 treatments using an O'Brien-Fleming (1979) stopping boundary (see Betensky 1996). Also, it is shown by DeLong (1980) to be the limiting distribution of a nonparametric test statistic for multiple regression. The approximations are compared with exact values from the literature and with values from a Monte Carlo simulation.

scholarly journals Fractionally integrated Bessel process

2021 ◽  
Vol 477 (2250) ◽  
pp. 20200934
Author(s):  
Georgiy Shevchenko ◽  
Dmytro Zatula
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hölder Continuity ◽  
Bessel Process ◽  
Holder Continuity ◽  
Basic Properties

We consider a fractionally integrated Bessel process defined by Y s δ , H = ∫ 0 ∞ ( u H − ( 1 / 2 ) − ( u − s ) + H − ( 1 / 2 ) ) d X u δ , where X δ is the Bessel process of dimension δ  > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.

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