在离散时间框架下时间t从0开始总时间T=4步长为1theta_t为风险负载因子gamma为风险厌恶系数alpha_t为索赔金额的均值beta_t^2为索赔金额的方差已知再保险策略q_t=fracleft1+theta_tright alpha_tgamma beta_t^2 prod_i=t+1^T-1 r_igamma=02theta_t=001alpha_t=02beta_t^2未知r_t=1

% 定义参数 T = 4; gamma = 0.2; theta = 0.01; alpha = 0.2; r = 1.0012;

% 计算q_t q = zeros(1, T); for t = 1:T beta = sqrt(q(t) * gamma * alpha^2 / ((1 + theta) * r^(T-t) * gamma)); q(t) = (1 + theta) * alpha / (gamma * beta^2 * r^(T-t)); end

% 作图 plot(q, beta^2); xlabel('q_t'); ylabel('\beta_t^2');