Whose money is the security deposit while the landlord is holding it?
Answered for: New York
§ 7-103. Money deposited or advanced for use or rental of real property; waiver void; administration expenses. 1. Whenever money shall be deposited or advanced on a contract or license agreement for the use or rental of real property as security for performance of the contract or agreement or to be applied to payments upon such contract or agreement when due, such money, with interest accruing thereon, if any, until repaid or so applied, shall continue to be the money of the person making such deposit or advance and shall be held in trust by the person with whom such deposit or advance shall be made and shall not be mingled with the personal moneys or become an asset of the person receiving the same, but may be disposed of as provided in section 7-105 of this chapter. 2. Whenever the person receiving money so deposited or advanced shall deposit such money in a banking organization, such person shall thereupon notify in writing each of the persons making such security deposit or advance, giving the name and address of the banking organization in which the deposit of security money is made, and the amount of such deposit. [...] 2-a. Whenever the money so deposited or advanced is for the rental of property containing six or more family dwelling units, the person receiving such money shall, subject to the provisions of this section, deposit it in an interest bearing account in a banking organization within the state which account shall earn interest at a rate which shall be the prevailing rate earned by other such deposits made with banking organizations in such area. [...] 3. Any provision of such a contract or agreement whereby a person who so deposits or advances money waives any provision of this section is absolutely void. 4. The term "real property" as used in this section is co-extensive in meaning with lands, tenements and hereditaments.
A security deposit stays the tenant's money and is held in trust by the landlord; it must not be mixed with the landlord's own funds or treated as the landlord's asset. If the landlord puts it in a bank, the landlord must tell the tenant in writing which bank and how much, and a lease clause waiving this section is void.
This answer is true in New York and nowhere else on this site. Another jurisdiction is another answer, or an honest gap: see what has been read for New York.