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未知theta_t=001alpha_t=02beta_t^2=004r_t=

代码如下：

T = 4;
dt = 1;
r = 1.0012;
theta = 0.01;
alpha = 0.2;
beta = sqrt(0.04);

gamma = linspace(0.1, 10, 100); % gamma取值范围
q = zeros(size(gamma)); % 初始化q

for i = 1:length(gamma)
    q(i) = (1 + theta) * alpha / (gamma(i) * beta^2 * prod(r.^(i+1:T-1)));
end

plot(gamma, q);
xlabel('\gamma');
ylabel('q_t');
title('Reinsurance Strategy');

运行结果如下：