Mathematical Finance in Continuous Time

2004 ◽  
pp. 229-288
Author(s):  
Nicholas H. Bingham ◽  
Rüdiger Kiesel
Keyword(s):  
Continuous Time ◽  
Mathematical Finance

FINANCIAL CALCULUS: AN INTRODUCTION TO DERIVATIVE PRICING

1998 ◽  
Vol 14 (3) ◽  
pp. 365-368
Author(s):  
Bent E. Sørenson
Keyword(s):  
Continuous Time ◽  
Differential Calculus ◽  
Mathematical Finance ◽  
Derivative Pricing ◽  
Symbolic Notation ◽  
Continuous Time Finance

“Notoriously, works on mathematical finance can be precise, and they can be comprehensible. Sadly, as Dr. Johnson might have put it, the ones which are precise are not necessarily comprehensible, and those comprehensible are not necessarily precise.” So starts the preface to Baxter and Rennie's recent treatise on financial calculus. The book attempts to give an introduction to modern continuous time finance in a precise and comprehensible fashion. Does it succeed? Yes, it is a very clear and precise little (233 pages) book, although the claim that the book is accessible to a reader with only “some knowledge of (classical) differential calculus and experience with symbolic notation” is exaggerated. Such a reader would find the material hard going indeed.

scholarly journals Summary Statistics for Endpoint-Conditioned Continuous-Time Markov Chains

2011 ◽  
Vol 48 (04) ◽  
pp. 911-924 ◽  
Author(s):  
Asger Hobolth ◽  
Jens Ledet Jensen
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Mathematical Finance ◽  
Alternative Methods ◽  
Eigenvalue Decomposition ◽  
Sequence Evolution ◽  
Summary Statistics ◽  
Continuous Time Markov Chains ◽  
Matrix Exponentials ◽  
Uniformization Method

Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behaviour, and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between two states, and the distribution of the total number of jumps) for discretely observed continuous-time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular, we develop a framework that allows for analyses of rather general summary statistics using the uniformization method.

scholarly journals Summary Statistics for Endpoint-Conditioned Continuous-Time Markov Chains

2011 ◽  
Vol 48 (4) ◽  
pp. 911-924 ◽  
Author(s):  
Asger Hobolth ◽  
Jens Ledet Jensen
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Mathematical Finance ◽  
Alternative Methods ◽  
Eigenvalue Decomposition ◽  
Sequence Evolution ◽  
Summary Statistics ◽  
Continuous Time Markov Chains ◽  
Matrix Exponentials ◽  
Uniformization Method

Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behaviour, and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between two states, and the distribution of the total number of jumps) for discretely observed continuous-time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular, we develop a framework that allows for analyses of rather general summary statistics using the uniformization method.

Mathematical Finance in Continuous Time

1998 ◽  
pp. 171-228
Author(s):  
Nicholas H. Bingham ◽  
Rüdiger Kiesel
Keyword(s):  
Continuous Time ◽  
Mathematical Finance

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Hierarchical Bayesian continuous time dynamic modeling.

2018 ◽  
Vol 23 (4) ◽  
pp. 774-799 ◽  
Author(s):  
Charles C. Driver ◽  
Manuel C. Voelkle
Keyword(s):  
Dynamic Modeling ◽  
Continuous Time ◽  
Hierarchical Bayesian ◽  
Time Dynamic
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