Optimal excess-of-loss reinsurance and investment with stochastic factor process

Author(s):  
Xiaoyu Kong ◽  
Yuhua Lü
Keyword(s):  
Author(s):  
Глафира Савицкая ◽  
Glafira Savitskaya

Theoretical bases of analysis of economic activity as a system of generalized knowledge about its subject, method, functions, principles, objectives and methods. Explores the analytical tools of the study; methodology of deterministic and stochastic factor analysis, financial calculations, methods of determining the value of on-farm reserves, the contents, functions, and methodological features of the main types of analysis issues of analysis at the enterprises. For students of higher educational institutions of economic specialties.


2018 ◽  
Vol 50 (01) ◽  
pp. 131-153 ◽  
Author(s):  
Hiroaki Hata ◽  
Shuenn-Jyi Sheu

AbstractWe consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of consumption and terminal wealth. We treat a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case in which the investor cannot observe the factor process and uses only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. We derive the Hamilton–Jacobi–Bellman equation. We solve this equation to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce the results obtained by the martingale method.


2019 ◽  
Vol 22 (6) ◽  
pp. 61-71
Author(s):  
M. G. Dobrosotskikh

There is show an experience of modern methods of scheduling in construction. There are reviewed existed scheduling methods: Critical Path Method, Constraints Programming, Job Shop Scheduling. Additionally there were reviewed methods with special edition for construction industry: shortest path planning, continue development frontline volume method, continue resources utilization method. All reviewed methods are simplified and don’t consider stochastic factors. Specific of the construction operation is a especially strong influence of stochastic factors to the construction production processes. There were reviewed methods of time reserve utilization, which appears in different stages of operations. This time reserve could be used, in particular, for minimization of negative aftereffects of stochastic factor influence on elements of construction. For these purpose was created target function of negative aftereffects minimization task, which describes dynamic and stochastic loses. The contribution of stochastic factors is expressed by exponential functions. There is shown, that redistribution of time reserve allows without any dynamic loses, to decrease contribution of stochastic loses. There is shown, that in approximation of independent works, the optimal schedule is that, which considers increasing of time reserve on critical directions. There is showed on individual example of algorithm for negative factors aftereffect minimization. Using this algorithm allows to make schedule with details of minimal approximated stochastic loses. In opposite, having a possibility of resources redistribution to directions, associated by high risks and loses, the optimal schedule plan will be alternative schedule plan, considering a possibility of operative redistribution, even through risks rise on non-critical directions.


2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Jianling Li ◽  
Diyi Chen ◽  
Hao Zhang ◽  
Jing Liu

Abstract This paper explores the stability of a hydro-turbine governing system (HTGS) under simultaneous effects of multistochastic factors. Specifically, three different sets of stochastic factors are introduced into the governing system, and the corresponding mathematical model with multistochastic factors is proposed. Then, seven cases are performed to reveal the dynamic characteristics of the governing system, including the excitations of only single stochastic factor, two stochastic factors, and three stochastic factors with different combinations of stochastic parameters. The results show some interesting phenomena. First, the stability of the system is weakened by introducing stochastic variables ω2 and ω3 into the inlet pressure of hydro-turbine (h2) and the bottom pressure of the surge tank (h3) separately, or both. Second, the negative effects of the stochastic characteristics of h2 and h3 on the governing system are reduced by introducing the stochastic variable (ω1) into the hydro-turbine flow (q1), on the basis of fully considering the influence of the stochastic characteristics of h2 and h3. Third, stochastic factors are generally considered to be unfavorable, but it may help the system to reach a global optimum status under certain conditions, which break through the habit of empirical thinking. Finally, this work not only provides a new insight for stochastic phenomena existing in engineering system, but also lays a theoretical basis for the safe and stable operation of the hydropower stations.


2016 ◽  
Vol 11 (01) ◽  
pp. 1650001 ◽  
Author(s):  
MOAWIA ALGHALITH ◽  
XU GUO ◽  
WING-KEUNG WONG ◽  
LIXING ZHU

In this paper we present two dynamic models of background risk. We first present a stochastic factor model with an additive background risk. Then, we present a dynamic model of simultaneous (correlated) multiplicative background risk and additive background risk. In so doing, we use a general utility function.


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