{"product_id":"ruin-probabilities-smoothness-bounds-supermartingale-approach-hardback-9781785482182","title":"Ruin Probabilities; Smoothness, Bounds, Supermartingale Approach (Hardback) 9781785482182","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eRuin Probabilities\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eSmoothness, Bounds, Supermartingale Approach\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003ePresents different continuous-time risk models for this branch of insurance mathematics\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eYuliya Mishura (Author), Olena Ragulina (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781785482182, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 10 October 2016\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e276 pages\u003cbr\u003e22.9 x 15.1 x 2.2 cm, 0.41 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\u003ci\u003eRuin Probabilities: Smoothness, Bounds, Supermartingale Approach\u003c\/i\u003e deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePart 1: Smoothness of the Survival Probabilities with Applications\u003c\/p\u003e \u003cp\u003e1: Classical Results on the Ruin Probabilities\u003c\/p\u003e \u003cp\u003e2: Classical Risk Model with Investments in a Risk-Free Asset\u003c\/p\u003e \u003cp\u003e3: Risk Model with Stochastic Premiums Investments in a Risk-Free Asset\u003c\/p\u003e \u003cp\u003e4: Classical Risk Model with a Franchise and a Liability Limit\u003c\/p\u003e \u003cp\u003e5: Optimal Control by the Franchise and Deductible Amounts in the Classical Risk Model\u003c\/p\u003e \u003cp\u003e6: Risk Models with Investments in Risk-Free and Risky Assets\u003c\/p\u003e \u003cp\u003ePart 2: Supermartingale Approach to the Estimation of Ruin Probabilities\u003c\/p\u003e \u003cp\u003e7: Risk Model with Variable Premium Intensity and Investments in One Risky Asset\u003c\/p\u003e \u003cp\u003e8: Risk Model with Variable Premium Intensity and Investments in One Risky Asset up to the Stopping Time of Investment Activity\u003c\/p\u003e \u003cp\u003e9: Risk Model with Variable Premium Intensity and Investments in One Risk-Free and a Few Risky Assets\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"ISTE Press - Elsevier","offers":[{"title":"Default Title","offer_id":46651735081240,"sku":"9781785482182","price":101.97,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781785482182.jpg?v=1696694799","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/ruin-probabilities-smoothness-bounds-supermartingale-approach-hardback-9781785482182","provider":"Freshly Printed Books","version":"1.0","type":"link"}