Optimal portfolio choice with path dependent benchmarked labor income: A mean field model

A pricing formula for delayed claims: appreciating the past to value the future

“…Our results demonstrate that SDDEs are valuable modeling tools that can address the findings of a large body of empirical literature on wage rigidity (e.g., [3,15,28,30]). Moreover, the results open the way to finding explicit solutions to interesting classes of lifecycle portfolio choice problems with state costraints (see [6,7,16]), as discussed in Sect. 3.…”

“…4 The setup described above can be extended to the case of payments over a bounded horizon in some interesting situations. When the payment stream is received until an exogenous Poisson stopping time τ δ (representing death or an irreversible unemployment shock when y represents labor income), expression (8) still applies, provided discounting is carried out at rate r + δ instead of r , where δ > 0 represents the Poisson parameter; see [6,7,16]. The case in which payments are received until a finite, deterministic time (capturing irreversible retirement when y represents labor income) can also be considered, at the price of additional technical work; see [5].…”

“…Another generalization of the problem addressed in [7] is considered in [16]. Similarly to [7], the authors consider a lifecycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky securities and a riskless asset subject to a borrowing constraint.…”

Representation of stochastic optimal control problems with delay in the control variable

“…Nevertheless, such a theory has been developed and is available for application (Fabbri et al 2017). For stochastic optimal control problems with a delay dependence on the state variable, but not on the control variable, see Biffis et al (2020), Biagini et al (2022), Djehiche et al (2022), De Feo et al (2023, Di Giacinto et al (2011), Federico (2011), Federico and Tankov (2015), Fuhrman et al (2010), Masiero and Tessitore (2022), Pang and Yong (2019). Se also ; Ren and Rosestolato (2020); for a different approach, where no representation in Hilbert space is performed, but the problem, presented in a path-dependent framework, is addressed via dynamic programming in the original setting, but making use of the so-called pathwise derivatives (see Cont and Fournie (2010a, b) for an account on this topic).…”

Wage Rigidity and Retirement in Optimal Portfolio Choice

“…The model is presented in Section 2. Beyond path-dependency (which is also treated in [5] and, in a different context, in [11]), the presence of finite retirement leads to two main technical problems: first, to express the borrowing constraints in a Markovian form that is suitable to attack the portfolio choice problem the approach used in [4] in the infinite retirement case is not applicable here); second, to solve an infinite dimensional stochastic optimal control problem with discontinuous dynamics and time dependent state constraints, a family of problems which, up to our knowledge, has not yet been treated in the literature. The first problem is solved in Section 3, where we need a non trivial technical work (part of it is relegated to the Appendix) to properly define the weights (g, h) which allow us to rewrite the borrowing constraint.…”