Optimal Portfolio of Corporate Investment and Consumption Problem under Market Closure: Inflation Case

<table>Relationship between the volatility of project A <svg height="8.3000002" id="M212" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.7250004 8.3000002" width="9.7250004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.038)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
</svg>, the inflation ratio <svg height="12.175" id="M213" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 8.5249996 12.175" width="8.5249996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M471 401q0 -32 -14 -91l-83 -376q-30 -146 -21 -180l-7 -15q-22 0 -47.5 23.5t-25.5 40.5q0 49 53 271l53 224q4 18 6.5 31t3.5 22.5t1 15t-2 9t-4.5 4.5t-6.5 1q-31 0 -100.5 -63.5t-126.5 -145.5q-16 -53 -40 -163q-48 -11 -74 -21l-7 8l82 341q9 36 -4 36
q-8 0 -28.5 -14t-38.5 -32l-17 22q41 43 85 71t66 28q23 0 23 -39q0 -19 -10 -64l-24 -103h2q77 101 201 182q37 24 74 24q31 0 31 -47z" id="x1D702"></path></g>
</svg>, and the optimal proportion <svg height="13.95" id="M214" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 17.775 13.95" width="17.775" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><path d="M574 449q-23 -58 -38 -79q-16 -4 -79 -4q-27 -100 -46 -219q-14 -87 7 -87t74 36l13 -27q-74 -81 -139 -81q-48 0 -48 62q0 22 8 59l60 258l-154 4q-21 -103 -54.5 -209t-64.5 -151q-38 -23 -83 -23l-7 15q46 36 94 152.5t64 216.5q-81 0 -138 -54l-18 23q22 27 39.5 43
t61.5 33.5t100 17.5q43 0 131.5 -2.5t129.5 -2.5q23 0 33.5 5t24.5 25z" id="x1D70B"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.113,5.525)"><path d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5
q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Optimal Portfolio of Corporate Investment and Consumption Problem under Market Closure: Inflation Case 