We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation.There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when shortselling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. E.g., for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum (2000), or with the case of no shortselling and no borrowing studied in Azcue and Muler (2009).
In the monograph, based on extensive statistical and operational information showing disparities in the development of social and economic functions of cities which have a serious negative impact on the recovery of economic growth in Russia, which is determined by the role of cities as centres of population (three quarters of the population of Russia) and most of the economic potential.
Imbalances in development of social and economic functions of cities in Russia can be attributed, the specifics of the historical path of our country, so have no analogue abroad. The rapidity of urbanization, utilization of limited resources primarily for industrial development, the policy needs of the population in Soviet times when the opposite rhetoric and more resulted in impaired development of social sphere of cities. The author identified and presented in the monograph rales imbalances in the development of social and economic functions of cities; the reasons for strengthening the destructive impact of imbalances in economic growth at the stages of social and technological transitions, one of which endures today Russia.
Integrated assessment modelling of multiparameter characteristics economic and social functions and determine the nature and extent of the imbalances in the book outlines basic principles of evaluation methodologies, algorithmic procedures and tools of functional urban typology based on the identities of the proportions of the social and economic development. The monograph presents results of the calculations carried out by the author on the basis of the developed methods to 115 cities in Russia, manufacturing centres. Showing the most profound disparities in urban development, impeding the formation of human capital and improve the quality of life of the population, essential attributes of the post-industrial society, towards which are all developed countries of the world, including Russia.
The book is built on the vast digital material has 44 drawing and table 49.. It is intended for specialists in the field of urban economy, teachers, students, and research staff.
^ Работа выполнена при частичной поддержке Российского фонда фундаменталь ных исследований (грант № 03-01-00479) и РАН по итогам 6-го конкурса-экспертизы проектов молодых ученых (грант №105).
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