1 Introduction
2 Motivation and discussion of the method
2.1 On the preference formulations
2.2 Why and when do we need a compromise?
2.3 The simultaneous evaluation approach
3 Application for retirement savings products
3.1 Motivation for the application
3.2 Financial market and considered products
3.3 Choice of the preference formulations
3.4 The combined preference function
3.5 Numerical analysis
3.5.1 Base case
3.5.2 Sensitivity analysis
3.5.2.1 Risk aversion and attitude
a | favorable compromise / preferable MCPT / EUT optimal | ||||
---|---|---|---|---|---|
\(\gamma\) | 0.1 | 0.3 | 0.5 | 0.7 | |
0.65 | K | \(\textit{*(60,42.5,1.14,3.23,3.75)}\) | \(\textit{*(60,42.5,1.14,3.26,3.75)}\) | \(\textit{*(60,42.5,1.14,3.28,3.75)}\) | \(\textit{*(60,42.5,1.14,3.3,3.75)}\) |
MCPT | \(*(60,40,1.43,3.21,3.77)\) | \(*(60,40,1.43,3.23,3.77)\) | \(*(60,40,1.43,3.25,3.77)\) | \(*(60,40,1.43,3.27,3.77)\) | |
EUT | \(\circ (100,37.5,-,3.56,0.04)\) | \(\circ (100,47.5,-,3.71,-0.03)\) | \(\circ (100,67.5,-,4,-0.2)\) | \(\circ (100,100,-,4.65,-0.55)\) | |
0.75 | K | \(\textit{*(60,45,0.82,3.25,4.08)}\) | \(\textit{*(60,47.5,0.49,3.31,4.05)}\) | \(\textit{*(60,47.5,0.49,3.34,4.05)}\) | \(\textit{*(60,47.5,0.49,3.38,4.05)}\) |
MCPT | \(*(60,45,0.82,3.25,4.08)\) | \(*(60,45,0.82,3.28,4.08)\) | \(*(60,45,0.82,3.31,4.08)\) | \(*(60,45,0.82,3.34,4.08)\) | |
EUT | \(\circ (100,37.5,-,3.56,0.22)\) | \(\circ (100,47.5,-,3.71,0)\) | \(\circ (100,67.5,-,4,-0.21)\) | \(\circ (100,100,-,4.65,-0.55)\) | |
0.88 | K | \({\textbf {*(60,50,0.14,3.29,4.79)}}\) | \({\textbf {*(60,50,0.14,3.33,4.79)}}\) | \({\textbf {*(60,72.5,-3.64,3.62,4.54)}}\) | \({\textbf {*(60,100,-9.38,4.1,4.32)}}\) |
MCPT | \(*(60,50,0.14,3.29,4.79)\) | \(*(60,50,0.14,3.33,4.79)\) | \(*(60,50,0.14,3.38,4.79)\) | \(*(60,50,0.14,3.42,4.79)\) | |
EUT | \(\circ (100,37.5,-,3.56,0.75)\) | \(\circ (100,47.5,-,3.71,0.36)\) | \(\circ (100,67.5,-,4,-0.07)\) | \(\circ (100,100,-,4.65,-0.55)\) | |
0.95 | K | \(\textit{*(60,92.5,-7.72,3.19,5.98)}\) | \(\textit{*(60,100,-9.38,3.41,6.12)}\) | \(\textit{*(60,100,-9.38,3.75,6.12)}\) | \(\textit{*(60,100,-9.38,4.1,6.12)}\) |
MCPT | \(*(60,100,-9.38,3.08,6.12)\) | \(*(60,100,-9.38,3.41,6.12)\) | \(*(60,100,-9.38,3.75,6.12)\) | \(*(60,100,-9.38,4.1,6.12)\) | |
EUT | \(\circ (100,37.5,-,3.56,1.16)\) | \(\circ (100,47.5,-,3.71,0.78)\) | \(\circ (100,67.5,-,4,0.28)\) | \(\circ (100,100,-,4.65,-0.55)\) |