应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2000年
4期
5-9
,共5页
随机控制%组合选择%受控扩散过程%不完备市场%存贷利率差%Hamilton-Jacobi-Bellman方程
隨機控製%組閤選擇%受控擴散過程%不完備市場%存貸利率差%Hamilton-Jacobi-Bellman方程
수궤공제%조합선택%수공확산과정%불완비시장%존대리솔차%Hamilton-Jacobi-Bellman방정
Stochastic control%Portfolio theory%Controlled diffusion process%Incomplete market%The rate difference on savings and loan%Hamilton-Jocobi-Bellman equation
本文讨论具有随机风险的公司的最优投资策略问题．公司投资选择是存款、贷款及股票交易．因市场的不完备性，公司在任一时刻均存在概率为正值的破产可能性．本文主要结果是：从贷款利率高于存款利率的实际出发，运用最优随机控制理论，得到使公司生存概率取最大值的最优投资策略，以及相应的最大生存概率，并对这些结果给出了严格证明．
本文討論具有隨機風險的公司的最優投資策略問題．公司投資選擇是存款、貸款及股票交易．因市場的不完備性，公司在任一時刻均存在概率為正值的破產可能性．本文主要結果是：從貸款利率高于存款利率的實際齣髮，運用最優隨機控製理論，得到使公司生存概率取最大值的最優投資策略，以及相應的最大生存概率，併對這些結果給齣瞭嚴格證明．
본문토론구유수궤풍험적공사적최우투자책략문제．공사투자선택시존관、대관급고표교역．인시장적불완비성，공사재임일시각균존재개솔위정치적파산가능성．본문주요결과시：종대관리솔고우존관리솔적실제출발，운용최우수궤공제이론，득도사공사생존개솔취최대치적최우투자책략，이급상응적최대생존개솔，병대저사결과급출료엄격증명．
This paper treats optimal investment policies for a firm with a random risk process. The flrm's choice on investment can be savings, loan and stock trading. As a fundamental incompleteness in the market, there is always a positive probability of ruin in the firm. The principal achievements are as follows: According to the fact that the interest rate on loan is higher than the one on savings, we acquire the optimal policies which maximize the survival probability, and this maximal survival probabihty. Furthermore, we have strictly proved these conclusions are right.
