{"product_id":"stochastic-risk-analysis-and-management-hardback-9781786300089","title":"Stochastic Risk Analysis and Management (Hardback) 9781786300089","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eStochastic Risk Analysis and Management\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eBoris Harlamov (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781786300089, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 3 March 2017\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e160 pages\u003cbr\u003e23.6 x 16.3 x 1.5 cm, 0.499 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe author investigates the Cramer –Lundberg model, collecting the most interesting theorems and methods, which estimate probability of default for a company of insurance business. These offer different kinds of approximate values for probability of default on the base of normal and diffusion approach and some special asymptotic.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eChapter 1 Mathematical Bases 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction to stochastic risk analysis 1\u003c\/p\u003e \u003cp\u003e1.1.1 About the subject 1\u003c\/p\u003e \u003cp\u003e1.1.2 About the ruin model 2\u003c\/p\u003e \u003cp\u003e1.2 Basic methods 4\u003c\/p\u003e \u003cp\u003e1.2.1 Some concepts of probability theory 4\u003c\/p\u003e \u003cp\u003e1.2.2 Markov processes 14\u003c\/p\u003e \u003cp\u003e1.2.3 Poisson process 18\u003c\/p\u003e \u003cp\u003e1.2.4 Gamma process 21\u003c\/p\u003e \u003cp\u003e1.2.5 Inverse gamma process 23\u003c\/p\u003e \u003cp\u003e1.2.6 Renewal process 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Cramér-Lundberg Model 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Infinite horizon 29\u003c\/p\u003e \u003cp\u003e2.1.1 Initial probability space 29\u003c\/p\u003e \u003cp\u003e2.1.2 Dynamics of a homogeneous insurance company portfolio 30\u003c\/p\u003e \u003cp\u003e2.1.3 Ruin time 33\u003c\/p\u003e \u003cp\u003e2.1.4 Parameters of the gain process 33\u003c\/p\u003e \u003cp\u003e2.1.5 Safety loading 35\u003c\/p\u003e \u003cp\u003e2.1.6 Pollaczek-Khinchin formula 36\u003c\/p\u003e \u003cp\u003e2.1.7 Sub-probability distribution G+ 38\u003c\/p\u003e \u003cp\u003e2.1.8 Consequences from the Pollaczek-Khinchin formula 41\u003c\/p\u003e \u003cp\u003e2.1.9 Adjustment coefficient of Lundberg 44\u003c\/p\u003e \u003cp\u003e2.1.10 Lundberg inequality 45\u003c\/p\u003e \u003cp\u003e2.1.11 Cramér asymptotics 46\u003c\/p\u003e \u003cp\u003e2.2 Finite horizon 49\u003c\/p\u003e \u003cp\u003e2.2.1 Change of measure 49\u003c\/p\u003e \u003cp\u003e2.2.2 Theorem of Gerber 54\u003c\/p\u003e \u003cp\u003e2.2.3 Change of measure with parameter gamma 56\u003c\/p\u003e \u003cp\u003e2.2.4 Exponential distribution of claim size 57\u003c\/p\u003e \u003cp\u003e2.2.5 Normal approximation 64\u003c\/p\u003e \u003cp\u003e2.2.6 Diffusion approximation 68\u003c\/p\u003e \u003cp\u003e2.2.7 The first exit time for the Wiener process 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Models With the Premium Dependent on the Capital 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definitions and examples 77\u003c\/p\u003e \u003cp\u003e3.1.1 General properties 78\u003c\/p\u003e \u003cp\u003e3.1.2 Accumulation process 81\u003c\/p\u003e \u003cp\u003e3.1.3 Two levels 86\u003c\/p\u003e \u003cp\u003e3.1.4 Interest rate 90\u003c\/p\u003e \u003cp\u003e3.1.5 Shift on space 91\u003c\/p\u003e \u003cp\u003e3.1.6 Discounted process 92\u003c\/p\u003e \u003cp\u003e3.1.7 Local factor of Lundberg 98\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Heavy Tails 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Problem of heavy tails 107\u003c\/p\u003e \u003cp\u003e4.1.1 Tail of distribution 107\u003c\/p\u003e \u003cp\u003e4.1.2 Subexponential distribution 109\u003c\/p\u003e \u003cp\u003e4.1.3 Cramér-Lundberg process 117\u003c\/p\u003e \u003cp\u003e4.1.4 Examples 120\u003c\/p\u003e \u003cp\u003e4.2 Integro-differential equation 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Some Problems of Control 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Estimation of probability of ruin on a finite interval 129\u003c\/p\u003e \u003cp\u003e5.2 Probability of the credit contract realization 130\u003c\/p\u003e \u003cp\u003e5.2.1 Dynamics of the diffusion-type capital 132\u003c\/p\u003e \u003cp\u003e5.3 Choosing the moment at which insurance begins 135\u003c\/p\u003e \u003cp\u003e5.3.1 Model of voluntary individual insurance 135\u003c\/p\u003e \u003cp\u003e5.3.2 Non-decreasing continuous semi-Markov process 139\u003c\/p\u003e \u003cp\u003eBibliography 147\u003c\/p\u003e \u003cp\u003eIndex 149\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52446332092696,"sku":"9781786300089","price":110.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781786300089.jpg?v=1785111098","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/stochastic-risk-analysis-and-management-hardback-9781786300089","provider":"Freshly Printed Books","version":"1.0","type":"link"}