# Andrea Andolfatto

**Biographical notes**

My name is Andrea Andolfatto and I am currently working at Algorand Fintech LAB, Bocconi University under the guidance of Professor Claudio Tebaldi.

I am a first year PhD student in Finance at Bocconi University and my interests lie in asset pricing in particular household finance and machine learning. You can download my cv here.

**Current Research Activity**

*Deep BSDE Lifecycle Portfolio Solver*

I am currently working on solving life cycle portfolio optimisation using machine learning. Considering the point of view of an intermediary with the objective to create a new product to enlarge the feasible solutions for a household. A household interested in the product would then assign an optimal weight to give to that particular product during different life stages. The consumption and investment weights are the main elements of the analysis and are the result of a given optimal policy function. The function can be approximated using reinforcement learning, in particular artificial neural networks.

In recent optimal lifecycle portfolio literature, the preferences of the agents, outlined in the utility function and its parameters are represented using time additive utilities for their convenience while using neural networks and having to define a loss function. In particular, the utility function parameters are set as hyperparameters in the optimisation of the consumption and investments optimal policy. The last elements of analysis are the products that are available to the household, which are part of the state variables in the life-cycle portfolio optimisation. The other selected state variables (i.e. income) are the ones that we think influence the household optimal policy function.

The life time utility optimization can also be seen as a system of backward stochastic differential equations (BSDEs), in particular forward BSDEs. This representation permits to take into consideration recursive utilities, which are more realistic and more robust with respect to the agents' preferences. Thus, we are interested in solving first analytically, as already defined in the present literature on BSDEs, and then numerically. In recent years reinforcement learning has been used to solve numerically the control variables of the BSDEs and has found applications especially in derivative pricing and risk management, solving the curse of dimensionality. For the lifecycle portfolio problem, ANNs are used to solve the system of BSDEs so to take into consideration more robust and realistic utilities function with respect to the current literature. Then, the model framework is extended to more complex cases to consider all the environment variables influencing the household portfolio decisions. We can concentrate on a relatively complex economic environment that includes realistic features of the investment problem that the typical European households face, as defined in the household finance and consumption survey. Thus, permitting us to compare the obtained optimal asset allocation, with the available products.

**Contacts**

andrea.andolfatto@phd.unibocconi.it

Ph.D. Student in Economics and Finance

Bocconi University, Via Roentgen 1, 2.b1 sr01, 20136, Milan, Italy