Semimartingale representation of fractional Riesz-Bessel motion

2001 ◽  
Vol 5 (1) ◽  
pp. 83-101 ◽  
Author(s):  
V.V. Anh ◽  
C.N. Nguyen
Keyword(s):  
Semimartingale Representation

Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates

1998 ◽  
Vol 35 (01) ◽  
pp. 115-123 ◽  
Author(s):  
A. Schöttl
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Explicit Solution ◽  
Random Time ◽  
Insurance Company ◽  
Markov Modulated ◽  
Semimartingale Representation

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.

scholarly journals A martingale view of Blackwell’s renewal theorem and its extensions to a general counting process

2019 ◽  
Vol 56 (2) ◽  
pp. 602-623
Author(s):  
Daryl J. Daley ◽  
Masakiyo Miyazawa
Keyword(s):  
Asymptotic Behaviour ◽  
Renewal Process ◽  
Stochastic Analysis ◽  
Counting Process ◽  
Intensity Function ◽  
Counting Processes ◽  
Renewal Theorem ◽  
Basic Tool ◽  
Semimartingale Representation ◽  
Blackwell's Renewal Theorem

AbstractMartingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and give extensions for various counting processes. We first consider a renewal process as a pilot example, deriving a new semimartingale representation that differs from the standard decomposition via the stochastic intensity function. We then revisit Blackwell’s renewal theorem, its refinements and extensions. Based on these observations, we extend the semimartingale representation to a general counting process, and give conditions under which asymptotic behaviour similar to Blackwell’s renewal theorem holds.

Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates

1998 ◽  
Vol 35 (1) ◽  
pp. 115-123 ◽  
Author(s):  
A. Schöttl
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Explicit Solution ◽  
Random Time ◽  
Insurance Company ◽  
Markov Modulated ◽  
Semimartingale Representation

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.

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