Abstract: Under the expected utility paradigm, the optimal investment and consumption problem was solved by Merton in 1969. His pioneering work adopting the expected utility framework inspired numerous optimality problems in various topics of actuarial and financial mathematics. The theory of indifference pricing is one of the representative instances. However, these elegant theories were built upon, first, fixing an investment and consumption horizon and, second, a priori assuming future utilities. In this talk, a recently developed notion called forward investment performance process by Musiela and Zariphopoulou will be introduced. With the element of consumption, SPDE and BSDE representations of forward investment and consumption performance processes will be presented. Properties and the large maturity behavior of forward entropic risk measures will be explored via BSDE representations.