Forecasting demands on bonds (Q2739844)

The author considers \(n\) bonds with nominals \(N_i\), prices \(p_i\), coupon rates \(g_i\) and payments at times \(t_i^1\),\dots, \(t_i^{k_i}\). It is shown that for an investor with the initial capital \(W\) and the utility \(U(x)=\sqrt{x}\) the optimal quality of \(i\)-th bond is NEWLINE\[NEWLINE Z_i={ {W b_ip_i^{-2}} \over {1+{b_1\over p_1}+\dots+{b_n\over p_n}}}, NEWLINE\]NEWLINE where NEWLINE\[NEWLINE b_i= \Biggl(\sqrt{N_i} \biggl(\sqrt{g_i}\sum_{j=1}^{k_i}\beta^{t_i^j}+\beta^{t_i^{k_i}} \biggr)\Biggr)^2, NEWLINE\]NEWLINE \(\beta\) being the discounting factor.